Intermediate frequency planning in radio transmitters and receivers

ABSTRACT

A method of intermediate frequency (i.f.) planning for radio transmitters and receivers involves predicting which i.f. or i.f. range will result in spurious emissions to or response from one or more “avoidance bands” being sources of unwanted signals or frequency bands closed to transmission, whereby to choose an i.f. or i.f. band which minimises such i.f. bands. The method may be carried out by computer software which may be embedded in a transmitter/receiver having means for varying its i.f.

[0001] The present invention relates to a method of determining thefrequency of operation of a local oscillator in a radio frequencytransmitter or receiver. Examples of such transmitters and receiversinclude mobile telephones, commercial radio receivers and short waveradio transmitters and receivers used in military applications. Theinvention is particularly applicable to front-end frequency convertersin both radio receiving and radio sending equipment, being eitherself-contained radios or the r.f. “front end” sub systems of otherequipment.

[0002] The invention is also applicable to single or double (or more)super-heterodyne architectures, the conversion nearest to the finalon-air frequency being of chief interest. In this case, the presentinvention is chiefly concerned with the intermediate frequency (i.f.)following (in a receiver) or preceding (in a transmitter) the finalon-air radio frequency. This frequency is termed hereinafter the “thefirst intermediate frequency” or “first i.f.”. The associated localoscillator is hereinafter referred to as the “first local oscillator”(1-LO).

[0003] Current radio frequency design centres on the sender and/orreceiver outline specification of the tuning range and the (first) i.f.bandwidth which must be fixed from the outset. Starting from thisspecification, the first intermediate frequency is often chosen from acatalogue on the questionable basis of:

[0004] a) Tradition;

[0005] b) How it was done last time;

[0006] c) Least trouble with commercial suppliers;

[0007] d) Catalogue price (not necessarily the same as cost in volumeproduction).

[0008] Then, after the radio's send and/or receive chain has beenelaborated, the spurious (unwanted) emissions and responses aredetermined, e.g. first image response/emission, local oscillator leakageand i.f. susceptibility. If any of the spurious emissions grossly exceedthe designer's electromagnetic compatibility (EMC) specification, theneither the whole frequency plan has to be re-worked or, more likely,extra engineering effort and cost must be expended. That usually entailstime consuming attempts to suppress the unwanted emissions in the caseof a radio transmitter, or, in the case of a radio receiver, theaddition of more protection against unwanted spurious responses. In bothcases, extra components can become necessary increasing the componentcount and consequently the bill of materials.

[0009] Thus, it is desirable to provide a method of radio frequencydesign centering on users' specifications and the spectral EMCrequirements of third parties. It would be preferable to provide amethod in which the tuning range and i.f. bandwidths need not be fixedat the very start of the design phase but can be left open for a while.

[0010] The preferred embodiment of the invention is a PC based utilityto expedite the choice of optimal first intermediate frequency for radiotransmitters and receivers. By way of background, the operation ofsuper-heterodyne radio receivers and senders will be briefly explainedwith reference to FIG. 1 which shows traditional block schematic designsfor a super-heterodyne radio receiver (top) and sender (below). In areceiver 20 the incoming radio frequency signal is passed through aroofing filter 21 to receive the wanted signal at frequency f. Thesignal is amplified by amplifier 22 and then mixed in mixer 23 with awaveform provided by local oscillator 24 at frequency f+z, z being theintermediate frequency. Thus, the mixer 23 yields the sum and differencefrequencies of the mixing process, i.e.

[0011] f+(f+z)=2f+z and

[0012] f−(f+z)=z.

[0013] The output signals from the local oscillator 24 are filtered byintermediate frequency bandpass filter 25 whereby the high frequencymixer products are excluded and only signals centred on frequency z areallowed to pass. The intermediate carrier frequency z is usually chosento be lower than the radio carrier frequency f. In general it is easierto implement subsequent amplification, filtering, sampling etc. of alower-frequency carrier than on a higher frequency carrier because, forexample, lower frequency components are less expensive. However, thereare certain applications in which the frequency z is higher than theradio frequency f. The frequency “z” is termed the intermediatefrequency whether it is above or below f because it is an intermediate,rather than final, frequency.

[0014] In a transmitter 30 signals to be transmitted, e.g. audio signalsare modulated in modulator 31 on to carrier frequency z and mixed inmixer 32 with signals at a frequency f+z from first local oscillator 33.Thus, mixer 32 yields sum and difference signals at frequencies

[0015] (f+z)−z=f and

[0016] (f+z)+z=f+2z

[0017] which signals are filtered at filter 34 to yield only signals atfrequency f to be amplified in amplifier 35, filtered in harmonic filter36 and transmitted from transmitter 37.

[0018] The foregoing describes arrangements in which the localoscillator tunes above the wanted frequency f, hereinafter termed“hi-mix”. In alternative receiver or transmitter arrangements the localoscillator may be tuned to a frequency below f, f-z, hereinafter termed“lo-mix”.

[0019] Optimisation of the first i.f. entails all the associatedfrequency translation choices, such as the local oscillator tuningrange, and whether it is a above (hi-mix) or below (low-mix) the band ofwanted signals to which the receiver is to be tuned. The underlyingassumption is that all of the major spurious emissions and responses canbe removed from an externally imposed protective band by a prudentchoice of mixing frequency plan. The invention is therefore a tool toaid internal frequency planning, enabling unlimited engineeringsolutions to external electromagnetic capability constraints.

[0020] In the following the terms “radio frequency transmitter” and“radio frequency receiver” are intended to encompass stand aloneequipment as well as the receiving and/or transmitting ends of otherequipment.

[0021] The conventional super-heterodyne principle is explained in moredetail in FIG. 2. FIG. 2 consists of two graphs, (a) illustrating thelo-mix scheme and (b) illustrating the hi-mix scheme. The shaded areasillustrate the dispositions of typical spectra of radio signals. Therectangles represent the band of frequencies passed by the band passfilter.

[0022] By means of a set of quantitative modifications, a newarchitecture known as “block conversion” can be derived from theconventional super-heterodyne architecture. It is known to be in use forradio reception but may equally be employed for sending.

[0023] Furthermore, hybrid architecture is postulated, bearingresemblance to both the conventional super-heterodyne and blockconversion principles.

[0024] The present invention is applicable to block conversion andhybrid architecture as well as the conventional super-heterodyne.

[0025] The derivation of block conversion is explained with reference tothe conventional super-heterodyne receiver of FIG. 1 (top). Thecomponents 21, 22 and 23 up to and including the first mixer/frequencychanger 23 remain as they are in a conventional implementation. Thefirst local oscillator now remains at a constant frequency irrespectiveof the particular channel to which it is desired to tune the radio. Allthe channels in a designated (wide) band (of width B) are down convertedin mixer 23 into a corresponding band of equal width B but lowerabsolute frequencies. Typically the band of lower frequencies occupies arange of +H to H+B, where H is an offset frequency, usually relativelysmall, achieved by arranging for the local oscillator 24 to be offsetfrom either the top or bottom edge of the r.f. band by the amount H.This principle is explained more clearly in the graphs of FIG. 3 inwhich (a) illustrates a lo-mix scheme and (b) illustrates a hi-mixscheme. Here the much wider band pass filter is shown embracing anaccordingly wide and complex radio signal—typically several channels. Inthe lo-mix arrangement the down converted spectrum is ordered in thesame sense as it had on air. In the hi-mix arrangement the spectrum isreversed on conversion, highest becomes lowest etc.

[0026] The i.f. band pass filter of the conventional radio (item 25) ishere replaced with a low pass filter, which transmits the wide band, ofwidth B+H, to base-band circuits and an analogue to digital converter.Once the base-band complex of signals has been sampled and rendered indigital form, a high speed sequence of binary numbers, powerful digitalsignal processing (DSP) can take over. The DSP performs the task ofresolving the complex spectrum into individual signals, selectingwhichever is desired, and recovering its communicated information.

[0027] In some implementations, the first mixer is replaced by a digitalsampling device, in which samples of the incoming waveform are taken atregular intervals, as determined by a sampling clock. As far as spuriousemissions, and image responses are concerned, the digital sampler isanalogous to the conventional mixer, and hence comes into the sameanalysis.

[0028] Despite those qualitative distinctions, block-conversion stillresembles the conventional architecture in that it:

[0029] i. can receive a plurality of radio signals across predefinedband (item 21);

[0030] ii. entails a mixing process, using a relatively strong 1LO, orsampling clock waveform;

[0031] iii. the frequency of the 1LO or sampling clock waveform isoffset by a relatively small frequency difference from wanted signals;

[0032] iv. that offset can be varied in each particular design (whetherstrictly i.f. in the conventional architecture, or some parametercorresponding to ‘H’ in block conversion);

[0033] V. the 1LO or sampling clock waveform can be set above the blockof wanted signals, or below, corresponding to the categories of “hi-mix”and lo-mix”;

[0034] vi. for each particular choice of offset (whether strictly i.f.in the conventional architecture, or some parameter corresponding to ‘H’to block conversion) there will be different sets of spurious responses,and different sets of spurious emissions to consider.

[0035] It will be appreciated that variations are possible between aconventional super heterodyne architecture on the one hand and fullblock conversion on the other, hereinafter referred to as hybridarchitectures. A hybrid would allow the first local oscillator to betuned whilst at the same time down converting a much wider band offrequencies than is ultimately required. An example of the operation ofa hybrid architecture is illustrated in FIG. 4.

[0036] Since the wide pass band of the band pass filter of a blockconversion or hybrid radio is equivalent to a range of intermediatefrequencies in a conventional radio, the references to intermediatefrequency should be considered hereinafter to apply equally to blockconversion or hybrid devices.

[0037] In a first aspect, the present invention provides a method ofdetermining an appropriate intermediate frequency or range ofintermediate frequencies for a radio frequency (r.f.) receiver in whicha received modulated r.f. signal is mixed with a signal from a localoscillator at a different frequency to yield as one of the mixingproducts a signal at a desired intermediate frequency for subsequentprocessing, the method comprising the steps of:

[0038] a) determining a tuning band of radio frequencies which thereceiver is desired to receive;

[0039] b) determining an avoidance band containing radio frequenciesclosed to external transmission and/or frequencies of sources of outsideinterference;

[0040] c) identifying a plurality of spurious mechanisms by which thereceiver either receives or transmits spurious signals and determiningthe frequencies of the spurious signals in relation to the intermediatefrequency; and

[0041] d) determining which intermediate frequencies result in spuriousemissions to or responses from the avoidance band for any of thefrequencies in the tuning band.

[0042] It follows from the foregoing that a similar method may be usedto design a radio frequency transmitter. Annexed claim 8 describes sucha method. Furthermore, the combined methods may be used to design atransceiver which may have different intermediate frequencies fortransmission and reception or the same front-end intermediate frequency.

[0043] It is already known to provide radio receivers with means forshifting the local oscillator frequency whilst the receiver is in use toavoid spurious signals for the particular radio frequency to which thereceiver is tuned. One example is shown in GB-A-2250877. By contrast,the present invention enables the prediction of spurious signals for thewhole of the tuning range prior to the design of the transmitter orreceiver whereby to avoid such spurious signals and avoid the need foradjustment of the local oscillator frequency each time a radio isre-tuned.

[0044] U.S. Pat. No. 5,752,174 discloses a radio selective callingreceiver having first and second local oscillators switchable between“high mix” and “low mix” (explained in more detail below) to achieve acombination that does not result in interference between the twooscillators for the received call signal frequency. Here theintermediate frequency itself is unchanged, and again the alteration oflocal oscillator configuration is done in response to a particular callfrequency. No attempt is suggested to design out such interference byconsidering the whole of the tuning range when selecting theintermediate frequency.

[0045] U.S. Pat. No. 5,689,819 discloses a transmitter-receiver circuitdesigned to mitigate interference between the transmitting and receivingsides. Only one spurious mechanism is taken into account, namely thewell-known first image. Furthermore there is no suggestion in thisdisclosure of determining a range of unsuitable intermediate frequenciesfor a tuning range rather than for a particular frequency to which theradio is tuned.

[0046] In contrast to the known methods described above, in the methodaccording to the invention the frequencies of spurious emissions arepredicted and the receiver/transmitter i.f. or local oscillatorfrequency (or frequency range for hybrid/block conversion) can then bepositively selected to avoid spurious emissions in the avoidance band.In the prior art, the tendency has been towards providing extra hardwareto remove spurious responses instead of managing the design such thatundesirable spurious responses do not appear in the first place.

[0047] Ideally the intermediate or local oscillator frequency should bechosen to avoid all unwanted (i.e. in the avoidance band) emissions orresponses but this is not always possible. It may be that there are noavailable l.o. or i.f. frequencies which avoid all unwanted emissions orresponses. In such a situation one possibility would be to simply pickan i.f. which eliminates as many of the spurious mechanisms as possible.This assumes that the spurious mechanisms are equally significant.Alternatively, in the preferred method the spurious mechanisms areranked, for example according to their effect on the performance of thereceiver/transmitter. Then, if it is not possible to choose anintermediate frequency (i.f.) which avoids all spurious responses fromor emissions to the avoidance band, an i.f. may be chosen, for example,that causes only the least significant spurious mechanism.

[0048] In the preferred embodiment of the invention, for each spuriousmechanism one or more ranges of intermediate frequency are determined,which do not result in emissions or responses in the avoidance band forthe whole of the tuned band. The range or ranges derived for eachmechanism are then superimposed, in a layered methodology, in the hopethat there is at least one range of available intermediate frequencywhich does not result in unwanted emissions or responses. If this is notthe case, the least significant of the spurious mechanisms can beeliminated, and if necessary this step repeated until an available rangeis found. The range of intermediate frequencies may be determined bymeans of a computer program. The program could operate automaticallyaccording to a predetermined ranking order or the order could bedetermined by an operator making suitable judgements as the designprocess proceeds.

[0049] A computer program product according to the invention could be anembedded object in a larger design program including also factors suchas cost of components, number of components etc. The speed of operationof the design process resulting from it being incorporated in a computerprogram renders this a practical design tool for iterative optimisationprocesses.

[0050] In a particularly advantageous embodiment of the invention, thespurious mechanisms are ranked according to their significance and arange of available intermediate frequencies is divided into sub rangesidentified by the most significant spurious mechanism, if any, resultingfrom the use of an intermediate frequency in that sub range. Then, ifthere is no “ideal” range, the appropriate range is the one resulting inthe least significant spurious response(s).

[0051] In the preferred method of the invention, for receiver ortransmitter, one or more hazard bands are determined for each spuriousmechanism, being ranges of frequency or spurious emissions or responseseach corresponding to the whole of the tuning band. The available rangesof i.f. can then be determined by ensuring that the hazard bands do notoverlap the avoidance band, for example using mathematical inversion offormulae defining the hazard bands.

[0052] The hazard bands and hence the range of available intermediatefrequencies may be determined by suitable computer software. Suchsoftware may be embedded in a radio receiver so that it is able toadjust its local oscillator/intermediate frequency according toprevailing conditions, for example a move from one country to anotherwhere the avoidance band is different. A transmitter/receiver would needmeans for receiving information that the avoidance band has changed.This could be pre-progranmued with avoidance band data for a certainnumber of countries in which it was likely to be used, so that theoperator would simply have to enter a country code for thetransmitter/receiver to re-tune itself to a suitable i.f. for thatcountry. Alternatively a receiver might have means for receivingbroadcast data relating to a change in avoidance band and responding tothat data by re-tuning if necessary. In some applications, e.g.:military, the transmitter/receiver might have means enabling a user toinput avoidance band data. Claim 35 describes a radio receiver accordingto the invention.

[0053] In the proposed modification of the invention, for use withblock-conversion architectures, an arbitrary choice of “i.f.” isdetermined by choosing the exact middle component of the band of wantedsignals. The other signals are then considered to be wide-bandextensions of the central signals, i.e. the sideband, having an extentof ±B/2. The new parameter, B/2, enters explicitly into a modified setof formulae, creating a species of “guard band” around the imposed“Avoidance bands”. With that minor difference, the wide-band versions ofthe formulae are very close to their counterparts in the narrow-bandversion. Likewise, the hybrid case can be accommodated by an extraparameter, “b”, the width of the wide band filter, where b is less thanB.

[0054] A preferred method according to the invention for a conventionalsuper-heterodyne transmitter or receiver will now be described by way ofexample only and with reference to the accompanying drawings in which:

[0055]FIG. 1 comprises two block schematic diagrams showing the maincomponents of a radio frequency receiver (top) and transmitter (below)

[0056]FIG. 2 shows two graphs illustrating the conventionalsuper-heterodyne principle with (a) indicating the lo-mix scheme and (b)indicating the hi-mix scheme;

[0057]FIG. 3 shows graphs corresponding to FIG. 2 for the blockconversion principle;

[0058]FIG. 4 shows graphs corresponding to FIG. 2 for a hybridarchitecture, lo mix only;

[0059]FIG. 5 is a graph showing the relationship between the tuned bandand a possible avoidance band for the purpose of explaining theparameters used in the method;

[0060]FIG. 6 is a graph showing the relationship between the localoscillator frequency and the first image bands.

[0061]FIG. 7 is a graph showing the output results of the method interms of spurious mechanism versus intermediate frequency;

[0062]FIG. 8 is a graph similar to FIG. 7 showing the results insimplified form;

[0063]FIG. 9 shows how apparatus according to the invention might beincorporated in a conventional super-heterodyne receiver;

[0064]FIG. 10 shows how apparatus according to the invention might beincorporated in a DSP radio receiver;

[0065]FIG. 11 shows how apparatus according to the invention might beincorporated in a software defined radio.

[0066] The method to be described below is particularly designed toscreen out eleven spurious mechanisms which may cause unwantedemissions, reception of unwanted signals or both. The method is intendedfor the design of transmitters and receivers and therefore deals withsome spurious mechanisms which effect only a transmitter or only areceiver. The relative importance of spurious mechanisms may varyaccording to the intended application for the transmitter or receiver.Thus, the ranking of the spurious mechanisms in terms of importance is atask for the operator. A typical ranking is shown in the table below.TABLE 1 Typical Ranking and Attribution of Spurious Mechanisms TASK RankMnemonic Spurious mechanism Tx→ Rx→ Rx← B 1 IMG ordinary image (first ✓✓ i.f.) C 2 LO1 local oscillator ✓ ✓ leakage D 3 IFL first i.f. leakage✓ ✓ E 4 S2A second image - closer ✓ F 5 S2B second image - ✓ further G 6S3A third image - closer ✓ H 7 S3B third image - further ✓ J 8 LA2second harmonic of 1 ✓ ✓ LO as affecting the avoidance band only K 9 LT2second harmonic of 1 ✓ ✓ LO as affecting the tuned band only U 10 SUMmixer sum product ✓ L 11 IMP third-order reverse ✓ ✓ inter-modulationproduct of 1 LO and ANY strong in-band carrier

[0067] The method starts from the assumption that there is a single bandof available frequencies for the radio frequency signal (the tuned band)and a single band of frequencies termed the “avoidance band” which areeither closed to radio frequency transmission or create a real source ofr.f. energy which might interfere with the performance of the productbeing designed. Not only must the frequency f be outside the avoidanceband but it is also necessary to ensure that any spurious emissions fromreceivers and transmitters are outside the avoidance band.

[0068] The method requires a minimum of input data, best understood byreference to FIG. 2. FIG. 2(a) illustrates the situation in which theband of available values for f is above the avoidance band and FIG. 2(b)illustrates the situation in which the band of available f is below theavoidance band. The graphs of FIG. 2 can be regarded as templates,hereinafter referred to as emc templates.

[0069] In FIG. 2 W represents the distance (in terms of frequency) fromthe bottom of one band to the bottom of the other, B is the band widthof the avoidance band, T is the width of the tuned band. The additionalvariable Γ represents the lowest (absolute) frequency to which thetransmitter/receiver can be tuned

[0070] Each of the eleven distinct spurious-generating mechanisms is aconsequence of a multiplicative, or otherwise non-linear electronicprocess in the time domain. For each elemental spectral requirement,i.e. at the lowest level of decomposition, there are two options in anysuper-heterodyne radio system. One is to make the local oscillator tuneabove the target (on-air) radio frequency, the other is to tune itbelow, termed “Hi-mix”, and “Lo-mix” respectively. That makes for 22possible formulations but there is another consideration.

[0071] In order to avoid the potentially messy use of negativequantities, two different sets of algebraic expressions have beenformulated to differentiate between avoidance bands above, and below theradio's tuning range.

[0072] On top of that, an allowance has been made for the twoalternative mixer architectures that primarily govern the radio'ssusceptibility to spurious responses and emissions. Thus, for eachspurious-generating mechanism, there can be up to four different sets offormula, called strategies, which are listed in the Table below TABLE 2Definition of Strategies avoidance band hi-mix lo-mix above a c below bd

[0073] Each of the two alternative spectral templates shown in FIG. 2can be met with a choice of two mixer strategies.

[0074] The causes of spurious emissions and responses in transmittersand receivers will be briefly explained below.

[0075] Images

[0076] In electronic mixers, such as items 23 and 32 in FIG. 1,frequency changing is achieved using the electronic equivalent ofmultiplying two time-domain periodic waveforms, usually sinusoids. Mostusefully one is the wanted signal, e.g. a sinusoid with arbitraryamplitude ‘a’, and the other is always a pure sinusoid with fixedamplitude, ‘b’ thus: wanted signal, at frequency signal(t) = a.cos(ω₁t)ω₁: pure sinusoid, at frequency stimulus(t) = b.cos(ω₂t) where t istime. ω₂:

[0077] The output of the frequency changer is the multiplicativeproduct:

signal(t) X stimulus(t)=½ a.b [cos(ω₁−ω₂).t+cos((ω ₁+ω₂).t]  Equation 1

[0078] The product contains terms representing the sum and differencesof the two contributing signals. At a radio receiver, it is thedifference signal that is required.

[0079] The receiver's i.f. band-pass filter is centred on the differencefrequency, z=|(ω₁−ω₂)|, so transmitting only the signal component, ½a.b. cos ((ω₁−ω₂).t The band-pass filter is conventionally fixed, so totune in the wanted signal at ω₁ the frequency, ω₂, of the stimulus isaltered, thus:

tuned frequency=ω₂ ±z  Equation 2

[0080] The“±z” is involved because (ω₁−ω₂) may be positive or negative,i.e. ω₁ may be above or below ω₂. So the frequency of the stimulus,actually the “local oscillator”, is given by:

ω₂=ω₁ ±z  Equation 3

[0081] Note that, in general, there are two frequencies that satisfyEquation 3; they are always equally disposed about the frequency of thelocal oscillator, and are termed “images” of one another.

[0082] An Example

[0083] Another, much more practical, way of performing the frequencychanging in a radio receiver, is to replace the local oscillatorsinusoid with a square wave at the same frequency. It may be stated thatthe corresponding mixer product will contain not only the sum anddifference terms as before but also an infinite series of unwantedsinusoids of amplitudes decreasing with increasing frequency. The squarewave itself can be represented as a sum to infinity of the sequence:

Square (ω₂ t)=b. cos (ω₂ t)+b/3. cos (3 ω₂ t)+b/5. cos (5 ω₂t)+  Equation 4

The mixer output=b.a(t) [ cos (ω₂−ω₁).t+⅓ cos (3ω₂−ω₁).t+⅕ cos(5ω₂−ω₁).t + . . . ]+b.a(t) [ cos (ω₂+ω₁).t+⅓ cos (3ω₂+ω₁).t+⅕ cos(5ω₂+ω₁).t + . . . ]  Equation 5

[0084] Assume a “hi-mix” option, so that ω₁<ω₂ and the wanted i.f. isz=ω₂−ω₁. The wanted i.f. (z) is passed through the succeeding band-passfilters that reject very strongly at all other frequencies. Depending onhow good the filters are, only an arbitrarily small, negligible amountof the higher-order terms is ever passed. However, should anotherexternal signal exist at frequency ω₃ then there could arise a situationwhere, for the same value of local oscillator (tuning the radio toreceive frequency ω₁), one of the higher-order terms converts theunwanted signal into the i.f. pass band, thus:

(3ω₂−ω₃)=z=(ω₂−ω₁

Hence

ω′₃=2.z+3.ω₁  Equation 6

[0085] If a “lo-mix” architecture had been chosen instead,

ω″₃=3.ω₁−4.z  Equation 7

[0086] The above result is typical of the moderately complicateddependence of the spurious responses on the choice of mixerarchitecture.

[0087] Bandwidth Considerations

[0088] Modulation

[0089] Up to now, the wanted r.f. and the translated i.f. have beentreated as pure sinusoids, or spectral lines of definite frequency andzero bandwidth. For the electrical disturbance to warrant the term“signal” it must carry some information, usually in the form ofmodulation. On a much longer time scale than the period of the sinusoidamplitude (or small frequency) variations may be superimposed; insignal(t) the constant multiplier ‘a’ can then be considered to bevarying with time, so that a=a(t). If stimulus(t) is generated by thelocal oscillator, then its multiplier, ‘b’, is kept constant so that theamplitude of the product is given by:

detector output=b.a(t)

[0090] a(t)=(detector output)/b—which is exactly what the user of theradio wants.

[0091] An important consequence of the modulation is the spectralbroadening of the otherwise pure sinusoid. Without modulation all theenergy is concentrated (mathematically) at definite frequency; withmodulation the energy is distributed over a small range of frequencies,giving rise a concept of bandwidth. The relative broadening is so slightthat for many purposes the r.f. and i.f. signals may still be thought ofas sinusoidal waveforms at a single frequency.

[0092] Selectivity

[0093] In addition to mapping the wanted off-air radio signal down to aconvenient i.f. for amplification, selectivity implies the rejection ofunwanted r.f. interference on other frequencies. Having determined(usually by international convention) a division of the radio spectruminto channels of definite bandwidth, off-air signals can be assessed asbeing either in-channel or else in adjacent channels with respect to thetuning of the receiver. That conception reflects the greater difficultyin rejecting radio energy that is at frequencies closest to the wantedfrequency.

[0094] The receiver ideally accepts all the energy in the tuned channeland rejects all the energy in all the channels on either side of it. Thereceiver's selectivity, is normally determined by a high-performanceband-pass filter, centred on the i.f. Only a narrow band of frequenciesaround the i.f. can be transmitted through the receiver and amplified.At increasing frequency offsets from z, e.g. z±y, the i.f. filterattenuates the spectral components until a large enough rejectionobtains at y=Y, let us say.

[0095] The i.f. filter's band-pass profile is effectively transferred tothe outside world, in as much as frequencies around the wanted carrierfrequency, f, are similarly attenuated. The receiver becomes less andless sensitive to other radio transmissions in, for example, adjacentchannels, at offsets of ±Y. The defence against interference breakingthrough is largely determined by the selectivity filter, or a cascade ofsuch filters.

[0096] Other non-linear Effects

[0097] There are four essential opportunities for non-linear distortion:

[0098] the off-air r.f. signal before being down converted in thefrequency changer;

[0099] the distortion of the local oscillator;

[0100] distortion of the i.f. signal in or just before its passagethrough the tuned amplifier;

[0101] amplification of the demodulated (base-band) wanted signal.

[0102] The second has been addressed already, and the last is of noconsequence to optimising the choice of i.f. The first and third are nowaddressed in reverse order.

[0103] Distortion in the Pass Band

[0104] The down-converted signal at i.f. will suffer harmonicdistortion, since it will be the only strong signal present. All thedistortion products will conform to second, third and so on harmonics,at 2z, 3z, 4z, 5z . . . In the normal situation, the fundamental, z,will be transmitted and amplified whilst the harmonics will beattenuated by the band-pass filter(s). For the same tuning of the localoscillator, there will, in general, be a (spurious) external radiofrequency, f(½) that gets down converted to z/2. The radio is deemed notto be tuned to f(½) because z/2 will not be passed by the i.f. stages ofthe receiver. However, if second harmonic distortion is present, aderived component will be at 2X(z/2)=z, and that will be amplified. Thereceiver will thereby have a spurious response to f(½), known as the“second image”. A new string of spurious responses using that mechanismarises in response to each significant harmonic of the i.f.

[0105] Front-end Distortion

[0106] The bandwidth of the r.f front end is, in general, wide enough tocatch many signals, wanted and unwanted. Any non-linear response fromfront-end amplifiers (including those outside the “radio” as an entity,such as antenna amplifiers) and even the first mixer will involvemultiple signals. Three types of distortion or non-linear processingneed to be distinguished:

[0107] when the wanted signal is strong and dominant, there willharmonic distortion, as described ABOVE

[0108] when there is an additional stronger, unwanted signal present, itmay cause de-sensitisation of the amplifier, and so modulate theamplitude of the wanted signal;

[0109] when two unwanted carriers are present, some of the products oftheir inter-modulation distortion may lie inside the pass band of thefront end.

[0110] The first can be rationalised out of existence; any harmonicdistortion of the input will give rise to new frequencies, which may betreated as a virtual “unwanted” signals, indistinguishable from trulyindependent unwanted r.f. interference. It merely multiplies theprobability that any arbitrary interfering carrier should hit a knownspurious response of the receiver; it doesn't add any new responses.

[0111] The second can cause annoyance, or even loss of reception butdoes not add to the list of spurious responses.

[0112] The last can operate in the absence of the wanted signal, or itcan totally overwhelm a weak wanted signal. The most commonlyencountered manifestation is third-order inter-modulation distortion.

[0113] Two-tone, Third-order Inter-modulation Distortion

[0114] The prerequisite for third-order inter-modulation distortion is anon-linear transfer characteristic of the polynomial form:

Output(t)=A.x(t)+B.x ³(t)  Equation 8

[0115] where x(t) is the input linear variable (current, electricalpotential)

[0116] Coefficient ‘A’ represents a wanted gain factor, and B representsthe potency for third-order inter-modulation distortion. Any non-linearterms in x²(t) have no effect but terms in x⁴(t), x⁵(t), etc. do.

[0117] For information, a corresponding fifth-order inter-modulationdistortion takes off from polynomials with terms in x⁵(t) and higher.The results from the following third-order analysis may be extrapolatedto fifth and so on.

[0118] Consider the (linear) addition of two sinusoidal carrierwaveforms, of equal amplitude for clarity:

Excitation, x(t)=cos (f ₁ t)+cos (f ₂ t) where f ₂ >f ₁ Output=A.[ cos(f ₁ t)+cos (f ₂ t)]+B.[( cos (f ₁ t)+cos (f ₂ t))³]  Equation 9

[0119] The component of the output corresponding to the ‘A’ terms inEquation 9 is just a magnified copy of x(t):

[0120] Corresponding to the ‘B’ term, will be a mass of trigonometricalterms, including cosines and sines of new frequencies, the 3^(rd)-orderinter-modulation products (i.m.p.):

[0121] F₁=2.f₁+f₂

[0122] F₂=2.f₁−f₂

[0123] F₃=f₁+2.f₂

[0124] F₄=|f₁−2.f₂|

[0125] The frequencies F₁ and F₃ being very large usually fall well outof harm's way. The other two, F₂ and F₄, cluster around the originalfrequencies f₁ and f₂, offset by (f₂−f₁) above and below them, thus:

upper i.m.p. F ₂ =f ₂+|(f ₂ −f ₁)|  Equation 10

lower i.m.p. F ₄ =f ₁−|(f ₂ −f ₁)|  Equation 11

[0126] That means that if (f₂−f₁) is relatively small, then the i.m.p.will probably also fall within the same pass band; ergo, they cannot befiltered out as easily as nominally “out-of-band” interfering signals.Hence, i.m.p. tend to be troublesome to radio. The fifth-ordercounterpart i.m.p. are removed by twice as much from the generatingtones, and so are slightly less of a problem from a frequency point ofview. In addition, the efficiency with which fifth-order i.m.p. can begenerated is much reduced compared to third-order.

[0127] The only i.m.p that can be generated in the i.f. amplifier mustbe derived from tones that are themselves close to the wanted if. Hence,the effect is merely to broaden out the selectivity of the receiver.Much more serious is the effect of i.m.d at the front end and in themixer. With much less restriction on input frequencies, it possible tohave a joint range tone pairs that create a F₂ or F₄ that falls exactlyon the i.f. Note that in this case the condition of the local oscillatoris irrelevant; the susceptibility is independent of the receiver tuning.Unlike many of the other spurious mechanisms, the receiver has a jointspurious tone-pair response, a continuum of frequencies that can floodthe receiver. Against this almost irremediable vulnerability is thestatistical improbability of the two tones possessing the criticalmutual relationship.

[0128] Correspondence Between Sender and Receiver

[0129] The chief difference between the sender and receiver is thatwhilst they both possess spurious emissions, only the receiver isdefined to have spurious responses. (NB receivers also emit energy atvery low levels).

[0130] Some of the mathematical relationships investigated above inrespect of radio receivers also govern the spurious emission of radiosenders. If the sender uses a super-heterodyne architecture, then thefrequency changer can also produce similar high-order mixer products asin Equation 5. The most ideal multiplicative mixer still produces animage, being the unused product in Equation 1. So-called image-rejectionmixers suppress the unwanted side band (first image) but that is at bestincomplete and its existence must still be noted.

[0131] Both sender and receiver may leak some of the powerful localoscillator drive, and to a lesser extent, the i.f. signal. Oftenstrongly clipped in the mixer circuit, the local oscillator signal isrich in harmonics and they too can leak to the outside world as spuriousemissions.

[0132] According to the invention, for each spurious mechanism, one ormore hazard bands is determined, being ranges of frequency of spuriousemissions or responses corresponding to the tuned band. The followingsection explains how the hazard bands are determined.

[0133] The 11 Spurious Mechanisms

[0134] General Note

[0135] The full list of spurious-generating mechanisms is given above.Each mechanism has a three-character mnemonic, a short title,designation as an emission or a response. Each is attributed to sender,receiver or both. The governing equations are derived for each mechanismin the following sub section. Reference is made to the key variablesused in the description of FIG. 5.

[0136] The formula are derived separately for each of the two mixerarchitectures, hi-mix and lo-mix, corresponding to strategies a and b,and c and d respectively.

[0137] Some mechanisms share a common theory and have been groupedtogether for analysis, e.g. the “closer” and “further” second images.However, every one of the eleven mechanisms, has its own third-levelsub-section containing the compact formulation.

[0138] For each canonical mechanism, the interim results will bepresented in tabular form, for consistency. TABLE 3 Paradigm for InterimResults Conditional Hazard band Strategy expression Impact from (loweredge) to (upper edge) A no conditions above 2Γ + z 2Γ + 2T + z B noconditions above 2Γ + z 2Γ + 2T + z c & d if {Γ > T2} BOTH 2Γ − z 2Γ +2T − z else n/a n/a

[0139] In most cases, the “Conditional expression” is superfluous butthere are some formulations where a logical test determines either thevalidity of the expression to its r.h.s., or decides between alternativeexpressions. In such instances, the tidiest way to encapsulate the totalformulation is in the form of:

[0140] if {logical expression} . . . [formula 1] else . . . [formula2/validity disclaimer]

[0141] A brief inspection of the formula for the hazard band showswhether the impact of the spurious is above or below the tuned band (orboth).

[0142] 1. First Image (IMG)

[0143] Theory

[0144] This is the only one of the eleven that is both a receiverresponse and a sender emission. It is helpful to consider first theaction in a sender with a super-heterodyne architecture, such as atypical short-wave (HF) transceiver. The signal modulation is applied tothe r.f. carrier by various electronic operations on a much higher i.f.,which is lowered to the wanted r.f. before being amplified and sent tothe antenna, etc.

[0145] The down conversion may be performed by mixing the i.f. signalwith the local oscillator waveform. Careful engineering approximates tothe situation represented by Equation 3, where two images are generated.Re-writing Equation 3:

f=ω ₂ ±z  Equation 12

[0146] where f is the wanted radio frequency to go out on air, and ω₂ isthe tuned frequency of the local oscillator (1 LO). The minus signindicates the case of interest here, so we may write, unambiguously:

ω₂ =f+z  Equation 13

[0147] Substituting Equation 13 back into Equation 12, the two imagefrequencies turn out to be:

[0148] the required on-air radio frequency,

(f+z)−z=f

[0149] the unwanted “first image” of frequency,

(f+z)+z=f+2z  Equation 14

[0150] Furthermore, as the frequency of the 1 LO is varied to make thetransmitted signal tune over other wanted frequencies, the first-imageoutput also moves about hazarding other users of the r.f. spectrum.

[0151] The image frequency can be suppressed by a number of means butnever entirely eliminated. Corresponding to the band of wantedfrequencies or channels to which the sender may be tuned, is an imageband, see FIG. 6. Unintended r.f. energy can be emitted anywhere in thisband depending on where the sender is tuned.

[0152] In Reception

[0153] In the case of this first-image phenomenon, the disposition ofthe frequencies involved remains unchanged when “receiver” issubstituted for “sender”; only the energy flow is reversed. The wantedfrequency, f, now becomes the centre of the channel to which thereceiver is tuned, and the first image, f+2z, a spurious channel towhich the receiver can also respond, simultaneously, as follows.

[0154] Hence, any incoming third-party transmissions at f+2z representan unguarded source of interference, which will be translated into thereceiver's first i.f. Mixing the wanted signal (at frequency f) with 1LO at (f+z) produces: z, and 2f+z, whereas mixing the unwanted imagefrequency, f+2z with the 1 LO produces z, and 2f+3z. Hence the detectedi.f. is determined by the energy content of both the wanted signal andthe unwanted interference in the “first image” channel.

[0155] The engineering investment behind the filter-based selectivity iscompletely circumvented by the first-image mechanism. It is almost as ifthe receiver were tuning in to another, spurious, frequency in thenormal way, and, indeed, the receiver is precisely as selectivitye aboutthis image response as it is about the normal channel.

[0156] Corresponding to the wanted band over which the receiver may betuned, is an image band, see FIG. 3. As the receiver is tuned over itsdesignated channels so it will also be susceptible to stray r.f. energyin the image band.

[0157] In both send and receive, the troublesome first images can bemitigated by interposing an extra wide band-pass passive filter (aroofing filter) between the antenna and the mixer. It serves to pass theband of wanted radio frequencies but attenuates heavily in the imageband. Such a filter is often subject to engineering-cost compromisesbecause it is more expensive to implement than the selectivity filter,having a wider pass band, and often being at a much higher frequency

[0158] Formulation

[0159] Hi-mix: Strategies a and b

[0160]FIG. 6 precisely illustrates this situation, expressing Equation14 for the sender example. As the radio frequency, f, tunes from Γ toΓ+T, the image travels in the same direction from Γ+2z to Γ+T+2z

[0161] Corollary 1 Hazard Band=Γ+2z to Γ+T+2z

[0162] Lo-mix: Strategies c and d

[0163] In the section entitled “Images”, Equation 3 expressed thepossibility of the local oscillator tuning below the wanted r.f. i.e. incontrast to FIG. 6. So by analogy:

ω₂ =f−z  Equation 15

[0164] Because the images are always equally disposed about the localoscillator the spurious first image is given by:

f(image)=ω₂ −|z| since the other image is the wanted, f=ω ₂ +|z|

Hence:

f(image)=(f−z)−z=f−2z  Equation 16

[0165] As the radio frequency tunes from Γ to Γ+T, the first imagetravels in the same direction from

Γ−2z to Γ+T−2z

[0166] Corollary 2 Hazard Band=Γ−2z to Γ+T−2z TABLE 4 Interimformulation, IMG Conditional Hazard band strategy expression Impact from(lower edge) to (upper edge) a no conditions above Γ + 2z Γ + T + 2z bno conditions above Γ + 2z Γ + T + 2z c no conditions below Γ − 2z Γ + T− 2z d no conditions below Γ − 2z Γ + T − 2z

[0167] 2. Local Oscillator Leakage (LO1)

[0168] Theory

[0169] This is a spurious emission mechanism, which can apply to bothsenders and receivers. The local oscillator is either above (hi-mix) orbelow (lo-mix) the tuned channel of the radio. Thus: hi-mix: ω₂ = f + zlo-mix: ω₂ = f − z

[0170] Formulation

[0171] As the radio tunes across its range, from Γ to Γ+T, so the 1 LOtravels in the same direction from: Hi-mix: strategies a and b Γ + z toΓ + T + z Lo-mix: strategies c and d Γ − z to Γ + T − z

[0172] Hence Table 5: TABLE 5 Interim formulation, LO1 ConditionalHazard band strategy expression Impact from (lower edge) to (upper edge)a & b no conditions above Γ + z Γ + T + z c & d no conditions below Γ −z Γ + T − z

[0173] This mechanism practically dominates the choice of i.f. and mustalways be included in any design run. The IMG mechanism allows values ofz down to T/2, where the first image will just come inside the tunedband. However, for T/2<z<T, permissible for IMG, the LO1 mechanism wouldtune the 1 LO inside the tuned band, quite unacceptably.

[0174] The assumption of restricting the i.f. such that z>T will be usedto simplify some of the later mechanisms.

[0175] 3. First I.F. Leakage (IFL)

[0176] Theory

[0177] This is a spot-frequency spurious receiver response only. It isquite independent of any other considerations, expressing the fact thatthe i.f. tuned amplifier is always vulnerable to r.f. carriers impingingon the radio at the precise same frequency.

[0178] Formulation

[0179] Regardless of which strategy is employed, the hazard band is justz (plus its proper bandwidth, b/w). It is reasonable to assume that, fora super-heterodyne radio architecture, the i.f. is chosen to be belowthe tuned r.f. TABLE 6 Interim formulation, IFL Hazard band Conditionalfrom (lower strategy expression Impact edge) to (upper edge) a, b, c, &d no conditions below z (less half i.f. z (plus half i.f. b/w) b/w) a,b, c, & d Special above* conditions*

[0180] *Rare exceptions can be cited, e.g. certain high-performanceshort-wave radio senders use a high i.f. in order to achieve widertuning range from the 1 LO.

[0181] Second Images

[0182] Theory

[0183] This is a receiver spurious response to a radio frequency thathas been down-converted to half the i.f., z/2. The second harmonic (seeabove under “distortion in the pass band”) of the half i.f. tone isexactly equal to the i.f. and can be passed as a legitimate signal. Fora particular tuning of the receiver, there are always two r.f. carriersthat can generate the half i.f.

[0184] For either a hi-mix or lo-mix architecture, both the tones:ω₂±z/2 produce a term at z/2 at the output of the mixer. The r.f. tonesare at f+z/2, and f+3z/2. A convenient distinction can be made (usefullater on) between “closer” and “further” second images.

[0185] For a hi-mix architecture, the local oscillator (ω₂=f+z) isalways above the wanted r.f., and so the image at f+z/2 lies midwaybetween them, and is termed the “closer” of the two. By contrast, theimage at f+3z/2 lies “further” away from the tuned r.f.

[0186] For a lo-mix architecture the spectral disposition is a mirrorimage. The closer image is now at f−z/2 and the further image is atf−3z/2. The four expressions for the second image have been re-groupedunder “closer” and “further” mechanisms, as follows.

[0187] 4. Second Image—Close (S2A)

[0188] The formulation for the hazard band is given in Table 7. TABLE 7Interim formulation, S2A Conditional Hazard band strategy expressionImpact from (lower edge) to (upper edge) a & b no conditions above Γ +z/2 Γ + T + z/2 c & d no conditions below Γ − z/2 Γ + T − z/2

[0189] 5. Second Image—Further (S2B)

[0190] The formulation for the hazard band is given in Table 8. TABLE 8Interim formulation, S2B Conditional Hazard band strategy expressionImpact from (lower edge) to (upper edge) a & b no conditions above Γ +3z/2 Γ + T + 3z/2 c & d no conditions below Γ − 3z/2 Γ + T − 3z/2

[0191] Third Images

[0192] Theory

[0193] As in the case of the second images, so the third harmonic of adown-converted spurious carrier can fall into the i.f. pass band. Thedown-converted tone is at z/3, so the r.f. tones are at: ω₂±z/3, thatis:

[0194] f±2z/3 for the closer images, and

[0195] f±4z/3 for the further images.

[0196] 6. Third Image—Closer (S3A)

[0197] The formulation for the hazard band is given in Table 9. TABLE 9Interim formulation, S3A Hazard band Conditional from (lower strategyexpression Impact edge) to (upper edge) a & b no conditions above Γ +2z/3 T + 2z/3 c & d no conditions below Γ − 2z/3 Γ + T − 2z/3

[0198] 7. Third Image—Further (S3B)

[0199] The formulation for the hazard band is given in Table 10. TABLE10 Interim formulation, S3B Hazard band Conditional from (lower strategyexpression Impact edge) to (upper edge) a & b no conditions above Γ +4z/3 Γ + T + 4z/3 c & d no conditions below Γ − 4z/3 Γ + T − 4z/3

[0200] General Multiple Images

[0201] For the m^(th) images, where m=1, 2, 3 . . . (viz including theconventional first image)

[0202] the general formula is: closer images: f ± (m − 1)z/m furtherimages: f ± (m + 1)z/m

[0203] For m=1, the two closer image expressions coalesce into thewanted tone at f, whilst the further images at f±z concur with thederivation in the “First Image” section above.

[0204] The attribution of the images follows the similar patternestablished for the second and third images.

[0205] 8,9. Second Harmonic of 1 LO (LA2 & LT2)

[0206] Theory

[0207] This is really a simple spurious emission concerning radioreceivers and senders, but the application to the spectral EMC templateis actually quite complex. Ergo, the actual process has been dividedartificially into two ostensible “mechanisms” for ease of coding. Itturns out that the separate application of these two “layered”mechanisms, LA2 and LT2, fairly straightforward by themselves,accomplishes the equivalent of a very complex algorithm, and one thatwould prove hard to verify.

[0208] One of the accepted constraints of the super-heterodynearchitecture is that the tuning range may not exceed the value of thefirst i.f. That keeps the local oscillator always above (hi-mix) orbelow (lo-mix) the receiver's tuning band, and enables any localoscillator leakage to be attenuated by the receiver's front-end“roofing” filter. It leads to an implicit requirement:

z≧T  Equation 17

[0209] For the hi-mix architecture, the local oscillator itself and itssecond harmonic are necessarily above the tuned band of the receiver (orsender) and the harmonic can interact only with the designated“avoidance” band (to be treated in below). That simpler case gives riseto the “avoidance band only” qualification of the LA2 mechanism, seeTable 1.

[0210] For the lo-mix architecture, the local oscillator is always belowthe tuned band, Γ to Γ+T, as constrained by Equation 17. However, thesecond harmonic (as also any higher harmonics) may fall into the tunedband under certain numerical conditions.

[0211] To keep things simple, a new “mechanism”, LT2, is coined thatignores the designated avoidance band of the EMC template, addressingonly the tuned band, Γ to Γ+T. Clearly, both mechanisms must be appliedin all cases to clear the possibility of:

[0212] interference to other users of the tuned band, including selfinterference if the receiver is tuned to the second harmonic of its ownlocal oscillator;

[0213] interference to other users of the avoidance band.

[0214] It is the successive application that effects the power of thismethod; successive elimination in effect implements the complex logicalmanipulations that would otherwise have required elaborate and obscurecoding.

[0215] Formulation (both LA2 and LT2) TABLE 11 Interim formulation, LA2and LT2 Hazard band Conditional from (lower strategy expression Impactedge) to (upper edge) a & b no conditions above 2Γ + 2z 2Γ + 2T + 2z c &d no conditions BOTH 2Γ − 2z 2Γ + 2T − 2z

[0216] 10. Mixer Sum Product (SUM)

[0217] Theory

[0218] This is a spurious emission that, in practice, concerns receiversonly. In Equation 1 the second term was ignored as not being ofpractical use for frequency changing in receivers. Whilst, therefore,unwanted it is none the less present and can be leaked back to theantenna. At the mixer it will have approximately the same strength asthe wanted i.f., so if a strong signal is received, then a comparativelystrong unwanted SUM tone may overcome the reverse-path attenuation andfilter attenuation to be re-radiated.

[0219] A numerically corresponding mixer product in the super-heterodynesender has already been addressed; in the framework of up-converting ani.f. to r.f. for emission, that component was designated a first image,see above. The receiver SUM product is distinct in frequency and originfrom the receiver's first image.

[0220] When the receiver is tuned to a wanted r.f.=f, then the localoscillator will be at: hi-mix: f + z lo-mix: f − z

[0221] The corresponding SUM terms are: hi-mix: 2f + z lo-mix: 2f − z

[0222] The lo-mix case the SUM could fall in the tuned band if the localoscillator goes sufficiently low. For practical radio designs, thatproblem can be eliminated by simply insisting, from the start, that:

ω₂(min)≧T

[0223] Therefore, the lowest SUM product that can arise is:

ω₂(min)+f(min)=(>T)+Γ  Equation 18

[0224] which is just above the top of the tuned band. Now, invokingEquation 17, simultaneously,

z≧T

[0225] Equation 18 can be re-written:

[f(min)−z]+f(min)=(>T)+Γ Γz+Γ=(>T)+Γ  Equation 19

[0226] From Equation 17, make the substitution, z>T in Equation 19:

Γ>2T  Equation 20

[0227] Equation 20 is actually a prerequisite for the feasibility of thelo-mix architecture. Another condition is implicit in Equation 19,

z<Γ−T  Equation 21

[0228] and again invoking Equation 17, the pre-condition on z becomes:

T<z<Γ−T  Equation 22

[0229] Equation 22 actually subsumes Equations 20 and 21.

[0230] Formulation

[0231] As the radio tunes across its range, from Γ to Γ+T, so the mixerSUM emission travels in the same direction across the following-Hazardbands: TABLE 12 Interim formulation, SUM Hazard band Conditional from(lower strategy expression Impact edge) to (upper edge) a & b noconditions above 2Γ + z 2Γ + 2T + z c & d if (Γ > 2T) BOTH 2Γ − z 2Γ +2T − z else: invalid - not applicable

[0232] Note that Equation 22 imposes a pre-condition on the spectralrequirements of the radio itself:

[0233] T<z<Γ−T which leads to a valid range of i.f. to choose from onlyif Γ>2T.

[0234] 11. Third-Order Reverse Inter-modulation Product Involving the 1LO (IMP)

[0235] Theory

[0236] This is a special kind of spurious emission from either areceiver or from a sender. It is to be distinguished from the morecommonly reported plain “reverse intermods” problem of broad-bandtransmitter power amplifiers. In that case, two strong, external,unwanted radio carriers impinge on the non-linear output circuits of theamplifier and generate i.m.p. The product, according to Equation 9, caneasily fall within the bandwidth of the amplifier, or the antennafilters, and be re-radiated.

[0237] The subject mechanism here, requires only one external carrier ofsufficient strength to produce inter-modulation distortion inconjunction with the already strong local oscillator tone. If theinterfering carrier is not a standard image of the wanted carrier, thenneither it nor the i.m.p. can be passed through the i.f. stages of thereceiver. However, the re-radiated i.m.p., (or reverse i.m.p.)constitutes an important spurious emission, one that is addressed by thepresent method.

[0238] Since it does not require the simultaneous presence of two strongr.f. carriers, it will certainly occur whenever the target radio comesclose to, or is approached by source of r.f. in the same radio band. Thefrequency of the reverse i.m.p. is determined by the tuning of the localoscillator, which in turn depends on the wanted tuned frequency, via thei.f., z.

[0239] In general, straddling the tuned band, are an asymmetrical pairof hazard bands in which the i.m.p. may occur. If the externalinterferer is effective only when it is within the radio's tuned band,then the bounds on both contributors to the i.m.p. are known. Theresulting hazard bands are then three times the width of the radio'stuning band. They separate from the tuned band as z increases but atdifferent rates; for every MHz increase in z, one travels 1 MHz, whilstthe other travels 2 MHz in the opposite direction.

[0240] Within each architecture (hi-mix, lo-mix) the spectral EMCtemplate will be concerned with only one of the i.m.p. hazard bands,hence the ensuing analysis is related to the application “strategy” asfollows: Strategy (a) hi-mix focus on upper hazard band; Strategy (b)hi-mix focus on lower hazard band; Strategy (c) lo-mix focus on upperhazard band; Strategy (d) lo-mix focus on lower hazard band.

[0241] In Strategies (b) and (c) the possibility of self interferencearises for normally acceptable ranges of z, i.e. z>T. In order to escapeit an extended condition is z>2T.

[0242] Common Frame for Analysis

[0243] It is convenient to define a new frame whose origin is at thelower edge of the tuned band, f₀=Γ. Let the frequency of the wanted r.f.channel be f_(R)=Γ+x, and that of the strong interferer be f₂=Γ+y. Theinter-modulation takes place between the strong interferer at f₂ and the1 LO (at f₁) corresponding to f_(R). The i.f. becomes a parameter to theformulation, since f₁=f_(R)±z.

[0244] Substituting in Equations 10 and 11 for the upper, and loweri.m.p. respectively, for f₂>f₁:

Upper i.m.p. F ₂ =f ₂+|(f ₂ −f ₁)|=Γ+y+|((Γ+y)−(Γ+x±z))|  Equation 23

Lower i.m.p. F ₄ =f ₁−|(f ²⁻ f ₁)|=Γ+x±z−|((Γ+y)−(Γ+x±z))|  Equation 24

[0245] Adapting Equations 10 and 11 for the upper, and lower i.m.p.respectively, for f₂<f₁:

Upper i.m.p. F ₂ =f ₁+|(f ₁ −f ₂)|=Γ+x±z+|((Γ+x±z)−(Γ+y))|  Equation 25

Lower i.m.p. F ₄ =f ₂−|(f ₁ −f ₂)|=Γ+y−|((Γ+x±z)−(Γ+y))|  Equation 26

[0246] For each equation, the hazard band is determined by finding thelower and upper bounds of F₂ (Strategies (a) and (c)), andF₄=(Strategies (b) and (d)).

[0247] In order to avoid difficulties with signs of algebraicquantities, etc. the inequalities appropriate to each Strategy areaddressed as special cases.

[0248] IMP Strategy (a)

[0249] The hi-mix choice dictates that f₁=f_(R)+z., hence f₁>f₂ forvalid bounds of x, and y and the normal requirement that z>T. Equation25 then becomes:

F ₂ =Γ+x+z+|(|+x+z−(Γ+y)|=Γ+|(2x+2z−y)|

[0250] The modulus, |(2x+2z−y)|, is always equal to the positiveexpression, 2x+2z−y, because z>0 so

F ₂=Γ+2x+2z−y

[0251] The upper edge of the resulting hazard band, F_(2(MAX)), ismanifested when the radio is tuned to the top of its range (x=T ) andthe interferer is at the lower edge (y=0). Hence, F_(2(MAX))=Γ+2T+2z

[0252] The lower edge of the hazard band, F_(2(MIN)), is manifested whenthe radio is tuned to the bottom of its range (x=0) and the interfereris at the upper edge (y=T). Hence, F_(2(MIN))=Γ+2z−T

[0253] The lower edge just touches the top of the tuned band, implying adegree of self-protection, provided (advisory) z>T. There are no otherpre-conditions (save for the implicit z>T condition).

[0254] IMP Strategy (b)

[0255] Equation 26 is applicable for the below-band i.m.p., using thesame hi-mix substitution as for Strategy (a):

F ₄ =f ₂−|(f ₁ −f ₂)|=Γ+y−|((Γ+x+z)−(Γ+y))|=Γ+y−|(x−y+z)|

[0256] The assumption is made that the LO1 mechanism rules out any caseswhere z<T for a sensible super-heterodyne architecture, so the contentsof the modulus, (x−y+z), must always be positive. The modulus operatorcan now be removed, keeping the implied positive sign.

F ₄=Γ+2y−x−z

[0257] The lower edge of the resulting hazard band, F_(4(MIN)), ismanifested when the radio is tuned to the top of its range (x=T) and theinterferer is at the lower edge (y=0). Hence, F_(4(MIN))=Γ−(T+z)

[0258] The upper edge of the hazard band, F_(4(MAX)), is manifested whenthe radio is tuned to the bottom of its range (x=0) and the interfereris at the upper edge (y=T). Hence, F_(4(MAX))=Γ+2T−z

[0259] As z is brought down to the value 2T, parametrically, so theupper edge of the hazard band approaches and then touches the bottom ofthe tuned band. In the normally permissible range t<z<2T, the hazardband actually overlaps the tuned band, implying that the IMP mechanismintroduces a new in-band source of interference. That can be avoided bysetting an extra, special restriction on z:

z>2T

[0260] It does not affect the validity of the formula (save for theimplicit z>T condition), and so is noted as “advisory” in Table 13.

[0261] IMP Strategy (c)

[0262] The lo-mix choice dictates that f₁=f_(R)−z., hence f₂>f₁ forvalid bounds of x, and y and the normal requirement that z>T. Equation23 then becomes:

F ₂ =f ₂+|(f ₂ −f ₁)|=Γ+y+|((Γ+y)−(Γ+x−z))|=Γ+y+|(y−x+z)|

[0263] The assumption is made that the LO1 mechanism rules out any caseswhere z<T for a sensible super-heterodyne architecture, so the contentsof the modulus, (x−y+z), must always be positive. The modulus operatorcan now be removed, keeping the implied positive sign.

F ₂=Γ+2y−x+z

[0264] The upper edge of the resulting hazard band, F_(2(MAX)), ismanifested when the radio is tuned to the bottom of its range (x=0) andthe interferer is at the top (y=T). Hence, F_(2(MAX))=Γ+2T+z

[0265] The lower edge of the hazard band, F_(2(MIN)), is manifested whenthe radio is tuned to the top of its range (x=T) and the interferer isat the bottom edge (y=0). Hence, F_(2(MIN))=Γ+z−T

[0266] As z is brought down to the value 2T, parametrically, so thelower edge of the hazard band approaches and then touches the top of thetuned band. In the normally permissible range t<z<2T, the hazard bandactually overlaps the tuned band, implying that the IMP mechanismintroduces a new in-band source of interference. For example, if z=3T/2,then the hazard band extends from +T/2 to 3½T.

[0267] That can be avoided by setting an extra, special restriction onz:

z>2T

[0268] It does not affect the validity of the formula (save for theimplicit z>T condition), and so is noted as “advisory” in Table 13.

[0269] IMP Strategy (d)

[0270] Equation 24 is applicable for the below-band i.m.p., using thesame lo-mix substitution as for Strategy (c):

F ₄ =f ₁−|(f ₂ −f ₁)|=Γ+x−z−|((Γ+y)−(Γ+x−z))|

[0271] The assumption is made that the LO1 mechanism rules out any caseswhere z<T for a sensible super-heterodyne architecture, so the contentsof the modulus, (x−y+z), must always be positive. The modulus operatorcan now be removed, keeping the implied positive sign.

F ₄=Γ+2x−y−2z

[0272] The lower edge of the resulting hazard band, F_(4(MIN)), ismanifested when the radio is tuned to the bottom of its range (x=0) andthe interferer is at the top (y=T). Hence, F_(4(MIN))=Γ−(T+2z)

[0273] The upper edge of the hazard band, F_(4(MAX)), is manifested whenthe radio is tuned to the top of its range (x=T) and the interferer isat the upper edge (y=0). Hence, F_(4(MAX))=Γ+2T−2z

[0274] The upper edge just touches the bottom of the tuned band,implying a degree of self-protection, provided (advisory) z>T. There areno other pre-conditions (save for the implicit z>T condition).

[0275] Summary of IMP formulations TABLE 13 Interim formulation, IMPConditional expression Hazard band (matches LO1 Advisory from (lower to(upper Strategy result) on ‘z’ Impact edge) edge) a z > T z > T above Γ− T + 2z Γ + 2T + 2z B z > T z > 2T below Γ − (T + z) Γ + 2T − z C z > Tz > 2T above Γ + z − T Γ + 2T + z D z > T z > T below Γ − T − 2z Γ +2T + 2z

[0276] Inverted Formulations

[0277] Survey of Data

[0278] The previous sections provide the set of expressions thatdetermine the top and bottom of all the hazard bands for eleven spuriousmechanisms. A hazard band can be defined completely once the radio'stuning range, mixer architecture and i.f. (z) have been specified.

[0279] The spectral EMC template introduces a means for predictingconflicts, such as harmful spurious emissions landing in radio-quietbands protected by law, or spurious receiver responses lying in bandsknown to contain active emissions. The present method envisages runningone template after another, each relating to one avoidance band, thussuccessively narrowing down the range of available i.f. The problemaddressed in the following section, is to reverse the processesconsidered hitherto, and discover those ranges of z that evade such EMCviolations, or compromises. By purely algebraic manipulations, it ispossible to ascertain the extreme values (min., max) that bound closedranges of z. At the boundary values, the top or bottom of a hazard bandtouches the lower or upper edge, respectively, of an avoidance band. Ingeneral, corresponding to the simplest template, there are two zones inwhich values of z avoid EMC conflict, the first being closed, and thesecond usually open-ended (to infinity). The first, running fromZ_(L)(min) to Z_(L)(max) has been termed the “lagoon”, the secondrunning, after a brief pause, from Z_(O)(min) to infinity (ocean);Z_(O)(min)>Z_(L)(max). (Note: the change of font for the canonicalbounds on z.)

[0280] In general, each Strategy needs its own inversion formulation.However not all need detailed analysis. The 44 cells in Table 14 havebeen screened on the following logical basis as either “trivial” orsubstantial. For the substantial combinations, the analysis is requiredis labelled by the “Method” number, for ease of reference.

[0281] Strategies (a) and (c) address an avoidance band above the tunedband, and hence have no interaction with spurious responses/emissionbelow the tuned band. The reverse applies for Strategies (b) and (d).Tables 1 to 13 state, for each Strategy, on which side of the tuned bandthe spurious response/emission has an impact. TABLE 14 Scope of formulainversions Mechanism Strategy (a) Strategy (b) Strategy (c) Strategy (d)IMG Method 1 trivial trivial Method 2 LO1 Method 3 trivial trivialMethod 4 IFL simple* Method 5 simple* Method 6 S2A Method 7 trivialtrivial Method 8 S2B Method 9 trivial trivial Method 10 S3A Method 11trivial trivial Method 12 S3B Method 13 trivial trivial Method 14 LA2Method 15 trivial Method 16 Method 17 LT2 trivial trivial Method 18Method 19 SUM Method 20 trivial Method 21 Method 22 IMP Method 23 Method24 Method 25 Method 26

[0282] *For the special case of IFL, the earlier assumption that thei.f. is much less than F has been re-introduced into the inversionformulation as an explicit simple condition.

[0283] For clarity every non-holonomic expression in the form: R−Sz<Twill be rendered: Sz>R+T, indicating a z>Z(min) result, and every one inthe form: U−Vz>X will be rendered: Vz<U−X, indicating a z<Z(max) result.

[0284] Methods of Algebraic Inversion

[0285] Method 1 (IMG, Strategy a)

[0286] No pre-conditions on z are assumed here, such as are dictated bythe pervasive LO1 mechanism. In fact the latter overrides the minimum,T/2, but that may be left to the point of application of LO1.

[0287] In the “lagoon”, there are two constraints on z, conditional uponthere being space sufficient for a spurious-hazard band between the topof the tuned band, Γ to Γ+T, and the bottom of the avoidance band, Γ+W.

[0288] The lower edge of the hazard band must exceed the top of thetuned band, hence:

[0289] Γ+2z>Γ+T

[0290] Result: Z_(L)(min)=T/2The upper edge of the hazard band must fallshort of the avoidance band, hence:

[0291] Γ+T+2z<Γ+W

[0292] Result: Z_(L)(max)=(W−T)/2{5}

[0293] For Z_(L)(max)>Z_(L)(min), W−T>T

[0294] Condition (lagoon): W>2TFor larger z, the lower edge of thehazard band must clear the top of the avoidance band, hence:

[0295] Γ+2z>Γ+W+B

[0296] Open-ended result: Z_(O)(min)>(W+B)/2

[0297] Method 2 (IMG, Strategy d)

[0298] No pre-conditions on z are assumed here, such as are dictated bythe LO1 mechanism. In fact the latter overrides the minimum, T/2, butthat may be left to the point of application of LO1.

[0299] In the “lagoon”, there are two constraints on z, conditional uponthere being space sufficient for a spurious-hazard band between thebottom of the tuned band, Γ to Γ+T, and the top of the avoidance band,Γ−W+B.

[0300] The upper edge of the hazard band must fall short of the bottomof the tuned band, hence:

[0301] Γ+T−2z<Γ ergo 2z>T

[0302] Result: Z_(L)(min)=T/2

[0303] The lower edge of the hazard band must clear the avoidance band,hence:

[0304] Γ−2z>Γ+B−W ergo 2z<W−B

[0305] Result: Z_(L)(max)=(W−B)/2

[0306] For Z_(L)(max)>Z_(L)(min), W−B>T

[0307] Condition (lagoon): W−B>T

[0308] For larger z, the upper edge of the hazard band must clear thebottom of the avoidance band, hence:

[0309] Γ+T−2z<Γ−W

[0310] Open-ended result: Z_(O)(min) (W+T)/2

[0311] Method 3 (LO1, Strategy a)

[0312] The lower edge of the hazard band must clear the top of the tunedband, hence:

[0313] Γ+z>Γ+T

[0314] Result: Z_(L)(min)=T

[0315] The upper edge of the hazard band must fall short of theavoidance band, hence:

[0316] Γ+T+z<Γ+W

[0317] Result: Z_(L)(MAX)=W−T

[0318] For Z_(L)(max)>Z_(L)(min), W−T>T

[0319] Condition (lagoon): W>2T

[0320] For larger z, the lower edge of the hazard band must clear thetop of the avoidance band, hence:

[0321] Γ+z>Γ+W+B

[0322] Open-ended result: z>W+B

[0323] Method 4 (LO1, Strategy d)

[0324] The upper edge of the hazard band must fall short of the bottomof the tuned band, hence:

[0325] Γ+T−z<F

[0326] Result: Z_(L)(min)=T

[0327] The upper edge of the hazard band must fall short of theavoidance band, hence:

[0328] Γ+T+z<Γ+W

[0329] Result: Z_(L)(max)=W−T

[0330] For Z_(L)(max)>Z_(L)(min), W−T>T

[0331] Condition (lagoon): W>2T

[0332] For larger z, the lower edge of the hazard band must clear thetop of the avoidance band, hence:

[0333] Γ+z>Γ+W+B

[0334] Open-ended result: z>W+B

[0335] Method 5 (IFL, Strategy b)

[0336] There is a direct restriction that z may not lie in the (lower)avoidance band, i.e. between Γ−W and Γ−W+B. A “lagoon” could be definedto be from zero to Z_(L)(max)=Γ−W, and then an open-ended range fromZ_(O)(min)=Γ−W+B but that would have to be capped before the bottom ofthe tuned band, etc. In practice such numerical proximities rarelyoccur, and it is sufficient to treat z as being subject to a singlemaximum, Z(max). Hence:

[0337] Result: Z(max)=Γ−W

[0338] Method 6 (IFL, Strategy d)

[0339] This follows the same method as Method 6, since the mixerarchitecture plays no part in this Mechanism. Note that this, and Method5, is one of the few results in which the absolute value of the tunedband, Γ, enters explicitly.

[0340] Result: Z(max)=Γ−W

[0341] Method 7 (S2A, Strategy a)

[0342] The lower edge of the hazard band must exceed the top of thetuned band, hence:

[0343] Γ+z/2>Γ+T

[0344] Result: Z_(L)(min)=2T

[0345] The upper edge of the hazard band must fall short of theavoidance band, hence:

[0346] Γ+T+z/2<Γ+W

[0347] Result: Z_(L)(max)=2(W−T)

[0348] For Z_(L)(max)>Z_(L)(min), 2(W−T)>2T

[0349] Condition (lagoon): W>2T

[0350] For larger z, the lower edge of the hazard band must clear thetop of the avoidance band, hence:

[0351] Γ+z/2>Γ+W+B

[0352] Open-ended result: Z_(O)(min)>2(W+B)

[0353] Method 8 (S2A, Strategy d)

[0354] The upper edge of the hazard band must fall short of the bottomof the tuned band, hence:

[0355] Γ+T−z/2<Γ ergo z>2T

[0356] Result: Z_(L)(min)=2T

[0357] The lower edge of the hazard band must clear the avoidance band,hence:

[0358] Γ−z/2>Γ+B−W ergo z<2(W−B)

[0359] Result: Z_(L)(max)=2(W−B)

[0360] For Z_(L)(max)>Z_(L)(min), 2(W−B)>2T

[0361] Condition (lagoon): W−B>T

[0362] For larger z, the upper edge of the hazard band must clear thebottom of the avoidance band, hence:

[0363] Γ+T−z/2<Γ−W

[0364] Open-ended result: Z_(O)(min)=2(W+T)

[0365] Method 9 (S2B, Strategy a)

[0366] The lower edge of the hazard band must exceed the top of thetuned band, hence:

[0367] Γ+3z/2>Γ+T

[0368] Result: Z_(L)(min)=2T/3

[0369] The upper edge of the hazard band must fall short of theavoidance band, hence:

[0370] Γ+T+3z/2<Γ+W

[0371] Result: Z_(L)(max)=2(W−T)/3

[0372] For Z_(L)(max)>Z_(L)(min), 2(W−T)>2T

[0373] Condition (lagoon): W>2T

[0374] For larger z, the lower edge of the hazard band must clear thetop of the avoidance band, hence:

[0375] Γ+3z/2>Γ+W+B

[0376] Open-ended result: Z_(O)(min)=2(W+B)/3

[0377] Method 10 (S2B Strategy d)

[0378] The upper edge of the hazard band must fall short of the bottomof the tuned band, hence:

[0379] Γ+T−3z/2<Γ ergo z>2T/3

[0380] Result: Z_(L)(min)=2T/3

[0381] The lower edge of the hazard band must clear the avoidance band,hence:

[0382] Γ−3z/2>Γ+B−W ergo z<2(W−B)/3

[0383] Result: Z_(L)(max)=2(W−B)/3

[0384] For Z_(L)(max)>Z_(L)(min), 2(W−B)/3>2T/3

[0385] Condition (lagoon): W−B>T

[0386] For larger z, the upper edge of the hazard band must clear thebottom of the avoidance band, hence:

[0387] Γ+T−3z/2<Γ−W

[0388] Open-ended result: Z_(O)(min)=2(W+T)/3

[0389] Method 11 (S3A, Strategy a)

[0390] The lower edge of the hazard band must exceed the top of thetuned band, hence:

[0391] Γ+2z/3>Γ+T

[0392] Result: Z_(L)(min)=3T/2

[0393] The upper edge of the hazard band must fall short of theavoidance band, hence:

[0394] Γ+T+2z/3<Γ+W

[0395] Result: Z_(L)(max)=3(W−T)/2

[0396] For Z_(L)(max)>Z_(L)(min), 3(W−T)/2>3T/2

[0397] Condition (lagoon): W>2T

[0398] For larger z, the lower edge of the hazard band must clear thetop of the avoidance band, hence:

[0399] Γ+2z/3>Γ+W+B

[0400] Open-ended result: Z_(O)(min)=3(W+B)/2

[0401] Method 12 (S3A, Strategy d)

[0402] The upper edge of the hazard band must fall short of the bottomof the tuned band, hence:

[0403] Γ+T−2z/3<Γ ergo z>3T/2

[0404] Result: Z_(L)(min)=3T/2

[0405] The lower edge of the hazard band must clear the avoidance band,hence:

[0406] Γ−2z/3>Γ+B−W ergo z<3(W−B)/2

[0407] Result: Z_(L)(max)=3(W−B)/2

[0408] For Z_(L)(max)>Z_(L)(min), 3(W−B)/2>3T/2

[0409] Condition (lagoon): W−B>T

[0410] For larger z, the upper edge of the hazard band must clear thebottom of the avoidance band, hence:

[0411] Γ+T−2z/3<Γ−W

[0412] Open-ended result: Z_(O)(min)=3(W+T)/2

[0413] Method 13 (S3B, Strategy a)

[0414] The lower edge of the hazard band must exceed the top of thetuned band, hence:

[0415] Γ+4z/3>Γ+T

[0416] Result: Z_(L)(min)=3T/4

[0417] The upper edge of the hazard band must fall short of theavoidance band, hence:

[0418] Γ+T+4z/3<Γ+W

[0419] Result: Z_(L)(max)=3(W−T)/4

[0420] For Z_(L)(max)>Z_(L)(min), 3(W−T)/4>3T/4

[0421] Condition (lagoon): W>2T

[0422] For larger z, the lower edge of the hazard band must clear thetop of the avoidance band, hence:

[0423] Γ+4z/3>Γ+W+B

[0424] Open-ended result: Z_(O)(min)=3(W+B)/4

[0425] Method 14 (S3B, Strategy d)

[0426] The upper edge of the hazard band must fall short of the bottomof the tuned band, hence:

[0427] Γ+T−4z/3<Γ ergo z>3T/4

[0428] Result: Z_(L)(min)=3T/4

[0429] The lower edge of the hazard band must clear the avoidance band,hence:

[0430] Γ−4z/3>Γ+B−W ergo z<3(W−B)/4

[0431] Result: Z_(L)(max)=3(W−B)/4

[0432] For Z_(L)(max)>Z_(L)(min), 3(W−B)/4>3T/4

[0433] Condition (lagoon): W−B>T

[0434] For larger z, the upper edge of the hazard band must clear thebottom of the avoidance band, hence:

[0435] Γ+T−4z/3<Γ−W

[0436] Open-ended result: Z_(O)(min)=3(W+T)/4

[0437] Method 15 (LA2, Strategy a)

[0438] As stated above, there is only an artificial distinction betweenthe LA2 and LT2 Mechanisms. The possibility of conflict between the LOharmonic and the tuned band is disregarded for this, LA2, analysis.

[0439] The structure to the z constraints could be described as aconditional lagoon. The open-ended range of z>Z_(O)(min) always exists;there is no pre-condition. However, the lagoon range, 0<z<Z_(L)(max)exists only if certain dimensions (Γ, T and W) of the EMC templatesatisfy a pre-condition.

[0440] The Open-ended Range

[0441] The lower edge of the hazard band must clear the avoidance band,hence:

[0442] 2Γ+2z>Γ+W+B

[0443] Ergo 2z>W+B−Γ

[0444] The r.h.s. can be positive, zero or negative, whereas z can bepositive only. Hence, if W+B−Γ<0, it is sufficient that z>0. In otherwords, ANY z is permissible.

[0445] If W+B−Γ>0 then a lower limit is set for z, i.e. z>Z_(O)(min).There is no need to define any pre-condition at all in this case.However, the non-holonomic expression needs to be split for coding,thus:

[0446] Result:

[0447] if (Γ<W+B)

[0448] then: Z_(O)(min)=(W+B−Γ)/2

[0449] else: Z_(O)(min)=0

[0450] The Lagoon

[0451] Here, the upper edge of the hazard band must fall short of thebottom of the avoidance band, hence:

[0452] 2Γ+2z+2T<Γ+W

[0453] Ergo 2z<(W−Γ−2T)

[0454] The requirement for the r.h.s. to be positive, (W−Γ−2T)/2>0 leadsto the pre-condition for the lagoon:

[0455] Γ<W−2T i.e. W>Γ+2T

[0456] then 2z<2Z_(L)(max)=(W−Γ−2T)/2

[0457] Result: Z_(L)(max)=(W−Γ−2T)/2

[0458] As a final check, compare Z(min) with Z_(L)(max):Z(min)−Z_(L)(max)=B+2T, which is always positive. Therefore, there isalways a finite separation between the open-ended and “lagoon” ranges ofz.

[0459] Method 16 (LA2, Strategy c)

[0460] The structure to the z constraints could be described as aconditional lagoon. The open-ended range of z>Z_(O)(min) always exists;there is no pre-condition. However, the lagoon range, 0<z<Z_(L)(max)exists only if certain dimensions (Γ, B and W) of the EMC templatesatisfy a pre-condition

[0461] The Open-ended Range

[0462] The upper edge of the hazard band must fall short of the bottomof the avoidance band, hence:

[0463] 2Γ−2z+2T>Γ+W

[0464] Ergo 2z>Γ+2T−W

[0465] The r.h.s. can be positive, zero or negative, whereas z can bepositive only. Hence, if Γ+2T−W<0, it is sufficient that z>0. In otherwords, ANY z is permissible.

[0466] If Γ+2T−W>0 then a lower limit is set for z, i.e. z>Z_(O)(min).There is no need to define any pre-condition at all in this case.However, the non-holonomic expression needs to be split for coding,thus:

[0467] Result:

[0468] if (Γ>W−2T)

[0469] then: Z_(O)(min)=(Γ+2T−W)/2else: Z_(O)(min)=0

[0470] The Lagoon

[0471] Here, the lower edge of the hazard band must exceed the top ofthe avoidance band, hence:

[0472] 2Γ−2z<Γ+W+B

[0473] Ergo z<(Γ−W−B)/2

[0474] The requirement for the r.h.s. to be positive, leads to thepre-condition for the lagoon:

[0475] Condition (lagoon): Γ>W+B

[0476] Result: z<Z_(L)(max)=(Γ−W−B)/2

[0477] As a final check, compare Z_(O)(min) with Z_(L)(max):Z_(O)(min)−Z_(L)(max)=B+2T, which is always positive. Therefore, thereis always a finite separation between the open-ended and “lagoon” rangesof z.

[0478] Method 17 (LA2, Strategy d)

[0479] Strictly, this Method describes a normal lagoon structure, with0<z<Z_(L)(max) in the lagoon, and z>Z_(O)(min) in the open-ended range.There are no pre-conditions. In practice this results in a simple upperlimit to z.

[0480] The Open-ended Range

[0481] The upper edge of the hazard band must fall short of the bottomof the avoidance band, hence:

[0482] 2Γ+2T−2z<Γ−W

[0483] Result: z>Z_(O)(min)=(W+2T+Γ)/2

[0484] The r.h.s. indicates a Z_(O)(min) that is always positive andimpracticably large.

[0485] The Lagoon

[0486] The lower edge of the hazard band must exceed the top of theavoidance band, hence:

[0487] 2Γ+2T−2z>Γ−W+B

[0488] Ergo 2z<Γ+W−B

[0489] In the EMC templates for Strategies (c) and (d), W>B -the spacebetween the tuned band and the (lower) avoidance band is W−B, which mustbe positive. So, in practice, there is no pre-condition on this lagoonstructure; it always exists.

[0490] Result: z<Z_(L)(max)=(Γ+W−B)/2

[0491] Method 18 (LT2, Strategy c)

[0492] This pseudo-mechanism is concerned solely with interference inthe tuned band and does not address any EMC avoidance band. Method 18 isprecisely the same as Method 19 except that it would be implemented inthe software under Strategy (c) in conjunction with Method 16(LA2—Strategy (c))

[0493] This Method describes a conditional lagoon structure, with0<z<Z_(L)(max) in the lagoon, and z>Z_(O)(min) in the open-ended range.

[0494] The Open-ended Range

[0495] The upper edge of the hazard band must fall short of the bottomof the tuned band, hence:

[0496] 2Γ+2T−2z<Γ

[0497] Result: z>Z_(O)(min) (Γ+2T)/2

[0498] The Lagoon

[0499] The lower edge of the hazard band must exceed the top of thetuned band, hence:

[0500] 2Γ−2z>Γ+T

[0501] Ergo 2z<Γ−T

[0502] Since the r.h.s. must be positive, the pre-condition is:

[0503] Condition (lagoon): Γ>T

[0504] Result: z<Z_(L)(max)=(Γ−T)/2

[0505] Method 19 (LT2, Strategy d)

[0506] This pseudo-mechanism is concerned solely with interference inthe tuned band and does not address any EMC avoidance band. Method 19 isprecisely the same as Method 18 except that it would be implemented inthe software under Strategy (d) in conjunction with Method 17(LA2—Strategy (d))

[0507] The Open-ended Range

[0508] Result: z>Z_(O)(min)=(Γ+2T)/2

[0509] The Lagoon

[0510] Condition (lagoon): Γ>T

[0511] Result: z<Z_(L)(max)=(Γ−T)/2

[0512] Method 20 (SUM, Strategy a)

[0513] The structure to the z constraints could be described as aconditional lagoon. The open-ended range of z>Z_(O)(min) always exists;there is no pre-condition. However, the lagoon range, 0<z<Z_(L)(max)exists only if certain dimensions (Γ, B and W) of the EMC templatesatisfy a pre-condition

[0514] The Open-ended Range

[0515] The upper edge of the hazard band must fall short of the bottomof the avoidance band, hence:

[0516] 2Γ+z>Γ+W+T

[0517] Ergo z>W+B−F

[0518] The r.h.s. can be positive, zero or negative, whereas z can bepositive only. Hence, if W+B−Γ<0, it is sufficient that z>0. In otherwords, ANY z is permissible.

[0519] If W+B−Γ>0 then a lower limit is set for z, i.e. z>Z_(O)(min).There is no need to define any pre-condition at all in this case.However, the non-holonomic expression needs to be split for coding,thus:

[0520] Result:

[0521] if (Γ>W+B)

[0522] then: Z_(O)(min)=(W+B−F)

[0523] else: Z_(O)(min)=0

[0524] The Lagoon

[0525] Here, the upper edge of the hazard band must fall short of thebottom of the avoidance band, hence:

[0526] 2Γ+2T+z<Γ+W

[0527] Ergo z<(W−2T−Γ)

[0528] The requirement for the r.h.s. to be positive, leads to thepre-condition for the lagoon:

[0529] Condition (lagoon): Γ<W−2T

[0530] Result: z<Z_(L)(max)<(W−2T−Γ)

[0531] Method 21 (SUM, Strategy c)

[0532] In practice, this Method describes a normal lagoon structure,with 0<z<Z_(L)(max) in the lagoon, and z>Z_(O)(min) in the open-endedrange. There are no pre-conditions.

[0533] The Open-ended Range

[0534] The upper edge of the hazard band must fall short of the bottomof the avoidance band, hence:

[0535] 2Γ+2T−z<Γ+W

[0536] Ergo z>Γ+2T−W

[0537] The r.h.s. can be positive, zero or negative, whereas z can bepositive only. Hence, if Γ+2T−W<0, it is sufficient that z>0. In otherwords, ANY z is permissible.

[0538] If Γ+2T−W>0 then a lower limit is set for z, i.e. z>Z_(O)(min).There is no need to define any pre-condition at all in this case.However, the non-holonomic expression needs to be split for coding,thus:

[0539] Result:

[0540] if (Γ>W−2T)

[0541] then: Z_(O)(min)=(Γ+2T−W) else: Z_(O)(min)=0

[0542] The Lagoon

[0543] The lower edge of the hazard band must exceed the top of theavoidance band, hence:

[0544] 2Γ−z>Γ+W

[0545] Ergo z<Γ−W

[0546] The requirement for the r.h.s. to be positive leads to thepre-condition, W>Γ.

[0547] Condition (lagoon): W>Γ

[0548] Result: z<Z_(L)(max)=Γ−W

[0549] Method 22 (SUM, Strategy d)

[0550] In practice, this Method yields a simple upper limit to z, since,on the lagoon analogy, the open-ended range of z (i.f.) would start wellabove the lower end of the tuned band. That option is hereby discarded.

[0551] The proof is given, for the sake of completeness.

[0552] The upper edge of the hazard band would have to fall short of thebottom of the avoidance band, hence:

[0553] 2Γ+2T−z′<Γ−W leading to z′>Γ+2T+W>Γ always.

[0554] What, then should have a lagoon, now becomes the simple upperlimit, thus:

[0555] The lower edge of the hazard band must exceed the top of theavoidance band, hence:

[0556] 2Γ−z>Γ−W+B

[0557] Ergo, z<Γ+W−B

[0558] In the EMC templates for Strategies (c) and (d), W−B>0, makingthe r.h.s. positive always

[0559] so that there is no pre-condition; the lagoon always exists.

[0560] Result: z<Z(min)=Γ+W−B

[0561] Method 23 (IMP, Strategy a)

[0562] This method produces an open-ended constraint, and a normallagoon. The lower limit in the lagoon is the obligatory z>T implicit inthe formula, which also matches the “advisory” lower limit of z>T asstated in Table 14.

[0563] Open-ended

[0564] The lower edge of the hazard band must exceed the top of theavoidance band, hence:

[0565] Γ−T+2z>Γ+W+B

[0566] Ergo, z>(W+T+B)/2

[0567] The “advisory” constraint, z>T, is superimposed, by formulatingthe equivalent of the Boolean logic:

[0568] [Z_(O)(min)≧(W+T+B)/2] AND [Z_(O)(min)≧T]

[0569] It is also partly covered if (W+T+B)/2>T i.e. if W+B>T, otherwisewe force Z_(O)(min)=T.

[0570] That non-holonomic logical expression needs to be split forcoding, thus:

[0571] Result:

[0572] if (W+B>T)

[0573] then: Z_(O)(min)=(W+T+B)/2

[0574] else: Z_(O)(min)=T

[0575] Lagoon

[0576] The upper edge of the hazard band must fall short of the bottomof the avoidance band, hence:

[0577] Γ+2T+2z<Γ+W

[0578] Ergo, 2z<W−2T

[0579] The r.h.s. must be positive for the lagoon to exist, hence thepre-condition, W>2T.

[0580] The additional “advisory” constraint is simply included byraising the threshold from zero to T. At the same time, any lagoons thatmay exist for 0<z<T are invalidated. The pre-condition may now betightened, thus:

[0581] 2z>2T

[0582] 2T<2z<(W−2T), ergo W>4T

[0583] Condition (lagoon): W>4T Result:

[0584] T<z<Z_(L)(max)=(W−2T)/2

[0585] Method 24 (IMP, Strategy b)

[0586] This method produces an open-ended constraint, and a normallagoon. The lower limit in the lagoon is the “advisory” lower limit ofz>2T as stated in Table 14, (not z>T implicit in the formula).

[0587] Open-ended

[0588] The upper edge of the hazard band must fall short of the bottomof the avoidance band, hence:

[0589] Γ+2T−z<Γ−W

[0590] Ergo, z>W+2T

[0591] The r.h.s. is always positive, ergo no pre-condition arises.

[0592] The “advisory” constraint, z>2T, is automatically covered,yielding the following plain expression:

[0593] Result: z>Z_(O)(min)=W+2T

[0594] Lagoon

[0595] The lower edge of the hazard band must exceed the top of theavoidance band, hence:

[0596] Γ−T−z>Γ−W+B

[0597] Ergo, z<W−T−B

[0598] The r.h.s. must be positive for the lagoon to exist, leading tothe pre-condition, W>T+B.

[0599] The additional “advisory” constraint is now included, by raisingthe threshold from zero to 2T. At the same time, any lagoons that mayexist for 0<z<2T are invalidated. The pre-condition may now betightened, thus:

[0600] 2T<z<W−T−B, ergo W>3T+B

[0601] Condition (lagoon): W>3T+B

[0602] Result: 2T<z<Z_(L)(max)=(W−T−B)

[0603] Method 25 (IMP, Strategy c)

[0604] This method produces an open-ended constraint, and a normallagoon. The lower limit in the lagoon is the “advisory” lower limit ofz>2T as stated in Table 14, (not z>T implicit in the formula).

[0605] Open-ended

[0606] The lower edge of the hazard band must exceed the top of theavoidance band, hence:

[0607] Γ−T+z>Γ+W+B

[0608] Ergo, z>W+T+B

[0609] The implicit constraint, z>T, is automatically covered the“advisory” constraint, z>2T. The “advisory” constraint, z>2T, is nowsuperimposed, by formulating the equivalent of the Boolean logic:

[0610] [Z_(O)(min)≧(W+T+B)] AND [Z_(O)(min)≧2T]

[0611] It is also partly covered if (W+T+B)>2T i.e. if W+B>T, otherwisewe force Z_(O)(min)=T.

[0612] That non-holonomic logical expression needs to be split forcoding, thus:

[0613] Result:

[0614] if (W+B>T)

[0615] then: Z_(O)(min)=(W+T+B)

[0616] else: Z_(O)(min)=2T

[0617] Lagoon

[0618] The upper edge of the hazard band must fall short of the bottomof the avoidance band, hence:

[0619] Γ+2T+z<Γ+W

[0620] Ergo, z<W−2T

[0621] The r.h.s. must be positive for the lagoon to exist, hence thepre-condition, W>2T.

[0622] The additional “advisory” constraint is now included by simplyraising the threshold from zero to 2T. At the same time, any lagoonsthat may exist for 0<z<2T are invalidated. The pre-condition may now betightened, thus:

[0623] 2T<z<W−2T, ergo W>4T

[0624] Condition (lagoon): W>4T

[0625] Result: 2T<z<Z_(L)(max)=(W−2T)

[0626] Method 26 (IMP, Strategy d)

[0627] This method produces an open-ended constraint, and a normallagoon. The lower limit in the lagoon is the implicit z>T, which alsocovers the “advisory” lower limit of z>T as stated in Table 14.

[0628] Open-ended

[0629] The upper edge of the hazard band must fall short of the bottomof the avoidance band, hence:

[0630] Γ+2T−2z<Γ−W

[0631] Ergo, z>(W+2T)/2=T+W/2

[0632] The r.h.s. is always positive, ergo no pre-condition arises.

[0633] Both the implicit and “advisory” constraint, z>T, isautomatically covered, yielding the following plain expression:

[0634] Result: z>Z_(O)(min)=(W+2T)/2

[0635] The lower edge of the hazard band must exceed the top of theavoidance band, hence:

[0636] Γ−T−2z>Γ−W+B

[0637] Ergo, z<(W−T−B)/2

[0638] The r.h.s. must be positive for the lagoon to exist, leading tothe pre-condition, W>T+B.

[0639] The additional “advisory” constraint is now included, by raisingthe threshold from zero to T. At the same time, any lagoons that mayexist for 0<z<2T are invalidated. The pre-condition may now betightened, thus:

[0640] 2T<2z<W−T−B, ergo W>3T+B

[0641] Condition (lagoon): W>3T+B

[0642] Result: T<z<Z_(L)(max)=(W−T−B)/2

[0643] Additional Formulations

[0644] At the current build state, versions of the present inventionimplement the eleven spurious-generating mechanisms described above.Several more mechanisms are considered to be suitable candidates for thenext software upgrade.

[0645] Chief among them are L3A and L3T, which do for the third harmonicwhat L2A and L2T do for the second harmonic of the 1 LO. It isconsidered next in order of importance because, whilst the radiofrequencies concerned will be further out from the tuned band, the levelof generation is strong.

[0646] In typical ring mixers, the local-oscillator (1 LO) waveform isgenerated at a high level and then used to over-drive the mixer diodes.The result is a voltage versus time waveform that approximates a squarewave, rich in odd-order harmonics, the third, fifth, etc. The even-orderharmonics represent an imbalance in the design of any ring mixer, oranalogous types. Hence, the second harmonic is a maverick case, thefailure to perfect the performance of the first mixer, whereas, thethird and other odd-order harmonics are unavoidable.

[0647] Analysis of Third Harmonic of 1LO

[0648] As with the treatment of the LA2 and LT2 Mechanisms, it turns outthat the separate application of two “layered” Mechanisms, LA3 and LT3,fairly straightforward by themselves, accomplishes the equivalent of avery complex algorithm, and one that would prove hard to verify.

[0649] One of the accepted constraints of the super-heterodynearchitecture is that the tuning range may not exceed the value of thefirst i.f. That keeps the local oscillator always above (hi-mix) orbelow (lo-mix) the receiver's tuning band, and enables any localoscillator leakage to be attenuated by the receiver's front-end“roofing” filter. It leads to an implicit requirement, z≧T (Equation 17)

[0650] For the hi-mix architecture, the local oscillator itself and itsthird harmonic are necessarily above the tuned band of the receiver (orsender) and the harmonic can interact only with the designated“avoidance” band. That simpler case gives rise to the “avoidance bandonly” qualification of the LA3 mechanism,.

[0651] For the lo-mix architecture, the local oscillator is always belowthe tuned band, Γ to Γ+T, as constrained by Equation 17. However, givena large enough z, the third harmonic (as also any higher harmonics) mayfall into the tuned band under certain numerical conditions. To keepthings simple, the pseudo “mechanism”, LT3, is coined that ignores thedesignated avoidance band of the EMC template, addressing only the tunedband, Γ to Γ+T. Clearly, both mechanisms must be applied in all cases toclear the possibility of:

[0652] interference to other users of the tuned band, including selfinterference if the receiver is tuned to the second harmonic of its ownlocal oscillator;

[0653] interference to other users of the avoidance band.

[0654] It is the successive application (e.g. inside TxRx_plannner) thateffects the power of this method; successive elimination in effectimplements the complex logical manipulations that would otherwise haverequired elaborate an obscure coding. TABLE 15 Third Harmonic of LocalOscillator Hazard band Conditional from (lower strategy expressionImpact edge) to (upper edge) a & b no conditions above 3Γ + 3z 3Γ + 3T +3z c & d no conditions BOTH 3Γ − 3z 3Γ + 3T − 3z

[0655] Following the pattern of the Mechanism inversion in Section 11.1,the only non-trivial strategies to consider are: (a), (c) and (d) forthe LA3, and (c) and (d) for the LT3.

[0656] As with the LA2 correspondent, the pre-condition, z>T, is assumedto have been imposed by the LO1 Mechanism, and will not be repeated herebelow.

[0657] LA3 Strategy (a)

[0658] The structure to the z constraints could be described as aconditional lagoon. The open-ended range of z>Z_(O)(min) always exists;there is no pre-condition. However, the lagoon range, 0<Z<Z_(L)(max)exists only if certain dimensions (Γ, T and W) of the EMC templatesatisfy a pre-condition.

[0659] The Open-ended Range

[0660] The lower edge of the hazard band must exceed the top of theavoidance band, hence:

[0661] 3Γ+3z>Γ+W+B

[0662] 3z>W+B−2F

[0663] The r.h.s. can be positive, zero or negative, whereas z can bepositive only. Hence, if 2Γ>W+B, it is sufficient that z>0. In otherwords, ANY z is permissible.

[0664] If 2Γ>W+B then a lower limit is set for z, i.e. z>Z_(O)(min).There is no need to define any pre-condition at all in this case.However, the non-holonomic expression needs to be split for coding,thus:

[0665] Result:

[0666] if (Γ>W+B)

[0667] then: Z_(O)(min)=(W+B−Γ)/3

[0668] else: Z_(O)(min)=0

[0669] The Lagoon

[0670] The upper edge of the hazard band must fall short of the bottomof the avoidance band, hence:

[0671] 3Γ+3T+3z<Γ+W

[0672] 3z<W−2Γ−3T

[0673] The r.h.s. must be positive for the lagoon to exist, hence thepre-condition, 2Γ<W−3T.

[0674] Condition (lagoon): W>2Γ+3T

[0675] Result: z<Z_(L)(max)=(W−2Γ−3T)/3

[0676] Corollary: either the open-ended, or the lagoon cases will yieldpractical values of z. The forbidden range between Z_(L)(max) andZ_(O)(min), when it exists, is (B+3T)/3.

[0677] LA3 Strategy (c)

[0678] In practice, the structure to the z constraints is a conditionallagoon. The open-ended range of z>Z_(O)(min) always exists but isimpractically high; there is no pre-condition.

[0679] The Open-ended Range

[0680] The upper edge of the hazard band must fall short of the bottomof the avoidance band, hence:

[0681] 3Γ+3T−3z<Γ+W

[0682] 3z>2Γ+3T−W

[0683] The r.h.s. can be positive, zero or negative, whereas z can bepositive only. Hence, if W>2Γ+3T, it is sufficient that z>0. In otherwords, ANY z is permissible.

[0684] If 2Γ>W−3T then a lower limit is set for z, i.e. z>Z_(O)(min).There is no need to define any pre-condition at all in this case.However, the non-holonomic expression needs to be split for coding,thus:

[0685] Result:

[0686] if (2Γ>W−3T)

[0687] then: Z_(O)(min)=(2Γ+3T−W)/3

[0688] else: Z_(O)(min)=0

[0689] The Lagoon

[0690] The lower edge of the hazard band must exceed the top of theavoidance band, hence:

[0691] 3Γ−3z<Γ+W+B

[0692] 3z<2Γ−W−B

[0693] The r.h.s. must be positive for the lagoon to exist, hence thepre-condition, 2Γ>W+B.

[0694] Condition (lagoon): Γ>(W+B)/2

[0695] Result: z<Z_(L)(max)=(2Γ−W−B)/3

[0696] The forbidden range between Z_(L)(max) and Z_(O)(min), when itexists, is (B+3T)/3.

[0697] LA3 Strategy (d)

[0698] Strictly, the structure to the z constraints is a lagoon. Theopen-ended range of z>Z_(O)(min) always exists but is impracticallyhigh; there is no pre-condition. In practice this results in a simpleupper limit to z.

[0699] The Open-ended Range

[0700] The upper edge of the hazard band must fall short of the bottomof the avoidance band, hence:

[0701] 3Γ+3T−3z<Γ−W

[0702] 3z>W+2Γ+3T always positive, and impractical to implement.

[0703] The Lagoon

[0704] The lower edge of the hazard band must exceed the top of theavoidance band, hence:

[0705] 3Γ−3z>Γ−W+B

[0706] 3z<2Γ+W−B

[0707] The r.h.s. must be positive for the lagoon to exist, hence thepre-condition, 2Γ>B−W.

[0708] In the EMC templates for Strategies (c) and (d), Γ>W>B hence ther.h.s. cannot but be positive; there is no pre-condition on the lagoon.

[0709] Result: z<Z_(L)(max)<(2Γ+W−B)/3

[0710] LT3

[0711] This pseudo-mechanism is concerned solely with interference inthe tuned band and does not address any EMC avoidance band. As before,(LT2), the following formulation is shared by both Strategy (c), andStrategy and (d).

[0712] The structure to the z constraints could be described as aconditional lagoon. The open-ended range of z>Z_(O)(min) always exists;there is no pre-condition. However, the lagoon range, 0<Z<Z_(L)(max)exists only if certain dimensions (Γ and T) of the EMC template satisfya pre-condition.

[0713] The Open-ended Range

[0714] The upper edge of the hazard band must fall short of the bottomof the tuned band, hence:

[0715] 3Γ+3T−3z<F

[0716] z>(3T+2F)/3-always large and positive, leading to anotherimpractical range of z.

[0717] The Lagoon

[0718] The lower edge of the hazard band must exceed the top of thetuned band, hence:

[0719] 3Γ−3z>Γ+T

[0720] z<(2Γ−T)/3

[0721] The r.h.s. must be positive for the lagoon to exist, hence thepre-condition, 2Γ>T, hence the pre-condition that T<Γ/2.

[0722] Condition (lagoon): Γ>2T

[0723] Result: z<Z_(L)(max)=(−T)/3

[0724] Other Harmonics of the 1 LO

[0725] Comparison of the formulations for LA2 and LA3, and LT2 and LT3indicates an induction formula. It is presented in Table 17 belowtogether with an example for the fifth harmonic. Note: m=(n−1). TABLE 16Induction formulation for higher harmonics of 1 LO Formula LA2 LA3 LA5LAn Strat (a) - open Z_(O)(min) (W + B − Γ)/2 (W + B − Γ)/3 (W + B −Γ)/5 (W + B − Γ)/n lagoon condition W > Γ + 2T W > 2Γ + 3T W > 4Γ + 5TW > mΓ + nT Strat (a) lagoon Z_(L)(max) (W − Γ− 2T)/2 (W − 2Γ − 3T)/3 (W− 4Γ − 5T)/5 (W − mΓ − nT)/n Strat (c) - open Z_(O)(min) (Γ + 2T − W)/2(2Γ + 3T + W)/3 (4Γ + 5T − W)/5 (mΓ + nT − W)/n lagoon condition Γ > W +B 2Γ > W + B 4Γ > W + B mΓ > W+ B Strat (c) lagoon Z_(L)(max) (Γ + W +B)/2 (2Γ −W − B)/3 (4Γ − W − B)/5 (mΓ − W − B)/n Strat (d) - openZ_(O)(min) (W + 2T + Γ)/2 (W + 3T + 2Γ)/3 (W+ 5T+ 4Γ)/5 (W + nT + mΓ)/nStrat (d) lagoon Z_(L)(max) (Γ + W − B)/2 (2Γ + − B)/3 (4Γ + W − B)/5(mΓ+ W− B)/n LTx Strat (c)/(d) LT2 LT3 LT5 LTn open-ended Z_(O)(min)(Γ + 2T)/2 (2Γ + 3T)/3 (4Γ + 5T)/5 (mΓ+ nt)/n lagoon condition Γ > T Γ >2T Γ > 4T Γ> mT lagoon Z_(L)(max) (Γ − T)/2 (2Γ − T)/3 (4Γ − T)/5 (mΓ−T)/n

[0726] As discussed in the introduction to this specification, themethod of the invention is preferably carried out with a suitablyprogrammed computer which is equipped with the formulae set out above. Agraphical user interface or GUI will guide a user through the stepsneeded to carry out the method. One possible operating process isdescribed below.

[0727] Let us assume that the computer is pre-programmed with theformulae for all of the eleven spurious mechanisms described above. As afirst step, the user will be asked to select which mechanisms are to beused in the process. Unless the product is a transceiver with identicalsend and receive intermediate frequencies, the selection of mechanismswill usually be a subset of the eleven, depending primarily on whetherproduct is a transmitter or receiver. The user may also at this stagerank the chosen mechanisms according to their significance although theprogram will usually have a default ranking order.

[0728] Having selected a plurality of spurious mechanisms, the user hasan opportunity to input an i.f. range. Next, the user defines theparameters Γ, T and W and B (see FIG. 5), and whether hi-mix or lo-mixis desired.

[0729] The computer program then uses the formulae discussed above todetermine which frequencies, from the full range of intermediatefrequencies input by the operator, result in spurious emissions to orresponses from the avoidance band for any part of the tuning range. Theoutput may be in the form of a graph with intermediate frequency alongone axis and on the other axis some indication as to which is the mostsignificant spurious mechanism for that i.f or i.f. range.

[0730] The process may then be repeated for additional avoidance bandssince in a practical situation there are usually several avoidancebands.

[0731] An exemplary set of results is illustrated in FIGS. 7 and 8. Inorder to generate these results, four avoidance bands were defined,namely:

[0732] (a) TV Band IV (to protect reception of third parties)

[0733] (b) GSM downlink (co-located transmitter emissions)

[0734] (c) DCS (digital cellular system) uplink (to protect nearbyreceivers)

[0735] (d) DCS downlink (nearby transmitter emissions)

[0736] Eight of the spurious mechanisms were considered as indicated onthe vertical axis of FIG. 7, ranked with the most significant (IMG) atthe bottom. FIG. 7 indicates that certain ranges of z give rise tospurious emissions responses to/from the avoidance bands as indicated.To facilitate the choice of z, the results may be presented as in FIG. 8with the most significant mechanism plotted against z. In the range of zfrom 0-500 MHz, there is one range of z that does not result in spuriousemissions responses between 352 MHz and 382 MHz. If there was no “clear”range, the operator might compromise the choice of z and decide that theleast significant spurious mechanism could be accepted (or possiblyscreened out by hardware). Thus if IMP was disregarded, the whole of therange from 160 to 447 MHz would be “clear”. Alternatively, if there wasno clear range the operator might repeat the process with a differentrange of z and/or a choice of hi/lo mix or a different tuning range.

[0737]FIG. 9 is a schematic diagram showing how a conventionalsuper-heterodyne receiver could be modified to incorporate apparatus forvarying the intermediate frequency according to prevailing conditions,Many of the components are the same as in FIG. 1, thus signals arereceived by receiving antenna 51, passed through roofing filter 52(which lets in only the wanted r.f. band) and amplified by front end lownoise amplifier 53 before being input to mixer 54. Here signals aremixed with a signal from a local oscillator 55 of variable frequency, tobe described in more detail below, and the output is filtered by aselected one of a bank of i.f. band pass filters 58, 59, 60 (more thanthree would be present in a practical example). The filter output isamplified again by amplifier 62 and subject to low frequency signalprocessing 63, demodulation and base band filtering before the useroutput e.g. audio is supplied as indicated at 70.

[0738] The receiver of FIG. 9 is additionally provided withmicroprocessor 72 which carries out the i.f. selection process discussedabove. The processor 72 may have a stored database 73 containing, forexample, electromagnetic compatibility data, and radio characteristicsof different countries. It uses this database information, together withoff-air broadcast information decoded by processor 75, to calculate asuitable intermediate frequency and/or whether the mix should be high orlow. The broadcast information may include, for example, the country inwhich the radio is now operating.

[0739] Information from the microprocessor 72 is conveyed to a tuningcontroller 66 which controls the frequency of local oscillator 55according to the selected value of z and whether the mix is high or low.The microprocessor output is also input to electronic switching 71 toswitch into operation the appropriate band pass filter 58, 59 or 60according to the choice of z.

[0740] In addition to tuning controller 66 the usual user operatedtuning controller 67 is provided to enable the user to tune to theappropriate r.f. for a selected channel.

[0741] The local oscillator 55 needs to be variable over a wide range tocover all intermediate frequencies and the fill r.f. tuning range. Sincethis would be a relatively expensive item then it might be replaced witha module having embedded synthesiser techniques.

[0742] In an alternative arrangement, a bank of electronically tunablefilters could replace items 58 to 60 being able to tune up to the lowerband of the next in order to cover a contiguous range of i.f. options.For any particular i.f. as indicated by the selection software, the mostsuitable tuned filter could then be switched in circuit and fine-tunedto the exact i.f. required. Then the local oscillator would be tuned toselect the wanted radio channel in exactly the same way as in FIGS. 2and 9.

[0743]FIG. 10 is a block schematic diagram showing how a blockconversion receiver might be modified to incorporate the presentinvention.

[0744] Signals received via antenna 101 are passed through wide bandroofing filter 102 and supplied to a down converter 103 which might be amixer or a digital sample-and-hold device. Converter 103 receives aninput from a local oscillator 104 or a clock generator for digitalsampling. A tuning controller 105 controls local oscillator 104according to the lo-mix/hi mix and frequency offset (H) choice (see FIG.3) determined by a microprocessor 120 carrying out the process of theinvention. The low pass filter 106 removes high mixer/sampler productsthat would cause aliasing to pass a band of down-converted signals whichare digitised in ADC 108 and processed by processor 109 to provide useroutput. Any broadcast off air information is also processed in processor120 and output to microprocessor 120 to determine the appropriate offsetH. The output is used by controller 105 to control the local oscillator104 as noted above and by tuning circuit 107 to tune the cut offfrequency of filter 106. A further tuner 111 is operable by the user toselect a channel for reception.

[0745] There are already proposals for future radios to be able toreconfigure their own hardware, under the control of embedded software,to handle different data formats and protocols. For exampleWO-A-99/09721 discloses a “self configuring multi-mode communicationsterminal”. FIG. 11 illustrates how the present invention might beemployed in such a radio.

[0746] The software defined architecture may be taken to exemplify thefuture of mobile radio transceivers, integrating DSP techniques andembedded software to the best advantage.

[0747] In FIG. 11, items 201,203 and 204 include the necessary set ofprotocol stacks (more than one is essential to any “softwareradio”).Likewise items 202, end user support, and 205, intelligentsupport, would be present in a software radio. More particularly,item204would include physical and data link reconfiguration resources aswell as software required to adjust other reconfigurable hardware in theradio receiver or sender. Reconfiguration of hardware would includetypes and parameters of modulators, demodulators, filter bandwidths,speed and precision of ADC and DAC and the tuning of the r.f. channelitself. It might and may also include smart-antenna technology, variableup-link and down-link frequency separations, band spreading techniquessuch as frequency hopping and/or direct sequence (e.g. CDMA), adaptivepower control, time-division duplexing, direction finding and otherlocation-related services effected through the r.f. bearer.

[0748] Item 206 represents an additional item not present in currentsoftware radio proposals, namely means receiving EMC information, suchas special band restrictions, local (country-specific) radioregulations, warnings of temporary radio interference. Looking evenfurther ahead, means possibly might exist for negotiation, hence thetwo-way arrows.

[0749] A data interface 207 interfaces between reconfigurable hardwareand the intelligent support. It is assumed to be handling data packetson both the down link (received off air), and on the up link (sent tothe local base station). The reconfigurable hardware is proposed forsoftware radios but in this example is separated into receiver hardware208 and sender hardware 209.

[0750] ADC 210 and DAC 211 are present with the ADC in the receiver, andthe DAC in the sender. In addition to whatever adjustments are alreadyneeded in a software radio (such as alteration of the clock rate, numberof bits of resolution), the real-time changes of i.f. determined by theembedded software according to the invention may also play a part indeciding clock rates, bit-resolution, decimation, etc. Not shown butinferred is the possible doubling up on DAC and ADC devices respectivelyin order to furnish I and Q channels for advanced modulation anddemodulation techniques. See also item 222 below.

[0751] Items 212 to 220 inclusive correspond to their symboliccounterparts in FIG. 1 and, together, constitute the receiving half ofthe “RF/IF” block. Items221 to 228 inc. make up the sender hardware, andconstitute the sending half of the “RF/IF” block. Items 212 and 228 hereshow separate antennas for receiving and sending. In some architectures(frequently for mobile transceivers) a common antenna serves bothreceiver and sender by means of either a duplexer (for full duplexcommunication systems) or antenna changeover switch (for two-way simplexsystems).

[0752] Item 221 could possibly be a synthesised local oscillator forconventional type modulators in item 222. In such case, the localoscillator would be tuned to the choice of i.f. selected by the methodof the invention for the sender (up link). Alternatively, item 221 mightbe the generator of a clock waveform to run the DSP modulator, item 222.

[0753] The functions of items 212 to 228 are analogous to those shown inFIG. 1 and will not be described in detail herein.

[0754] Item 222: In more advanced, fully digital modulation schemes, thesignal modulation may be generated by direct signal synthesis, replacingthe need for item 211. The centre frequency of the resulting signal,corresponding to the sender's first i.f., would, in that case, bedetermined by DSP algorithms in combination with the frequency of aclock waveform, see item 221.

1. A computer program product comprising a computer readable mediumhaving thereon computer program code means, when said program is loaded,to make the computer execute, when supplied with at least tuning bandand avoidance band data, a method of determining an appropriateintermediate frequency or intermediate frequency range for a radiofrequency (r.f.) receiver in which a received modulated r.f. signal ismixed with a signal from a local oscillator at a different frequency toyield as one of the mixing products a signal at a desired intermediatefrequency for subsequent processing, the method comprising the steps of:a) determining a tuning band of radio frequencies which the receiver isdesired to receive; b) determining an avoidance band containing radiofrequencies closed to external transmission and/or frequencies ofsources of outside interference; c) identifying a plurality of spuriousmechanisms by which the receiver either receives or transmits spurioussignals and determining the frequencies of the spurious signals inrelation to the intermediate frequency; and d) determining whichintermediate frequencies result in spurious emissions to or responsesfrom the avoidance band for any of the frequencies in the tuning band.2. A computer program product as claimed in claim 1 in which step (d)includes determining, for each spurious mechanism, one or more hazardbands, being ranges of frequency of spurious emissions or responses eachcorresponding to the whole of the tuning band.
 3. A computer programproduct as claimed in claim 1 in which the spurious mechanisms includeone of the second images.
 4. A computer program product as claimed inclaim 1 in which the spurious mechanisms include both of the secondimages.
 5. A computer program product as claimed in claim 1 in which thespurious mechanisms include one of the third images.
 6. A computerprogram product as claimed in claim 1 in which the spurious mechanismsinclude both of the third images.
 7. A computer program product asclaimed in claim 1 in which the spurious mechanisms include the mixersum product.
 8. A computer program product comprising a computerreadable medium having thereon computer program code means, when saidprogram is loaded, to make the computer execute, when supplied with atleast tuning band and avoidance band data, a method of determining anappropriate intermediate frequency or intermediate frequency range for aradio frequency transmitter in which a modulated signal at anintermediate frequency is mixed with a local oscillator waveform havinga different frequency to yield as one of the mixing products a signal ata desired frequency for transmission, the method comprising: a)determining a tuning band of frequencies which the transmitter isdesired to transmit; b) determining an avoidance band containing radiofrequencies closed external transmission; c) identifying a plurality ofspurious mechanisms by which the transmitter transmits spurious signalsand determining the relationship between the spurious signals and theintermediate frequency; and d) determining which intermediatefrequencies result in spurious emissions to the avoidance band for anyof the frequencies in the tuning range.
 9. A computer program product asclaimed in claim 8 in which step (d) includes determining, for eachspurious mechanism, one or more hazard bands being ranges of frequencyof spurious emissions each corresponding to the whole of the tuned band.10. A computer program product as claimed in claim 1 including the stepof determining one or more additional avoidance bands and repeating step(d) for each additional avoidance band.
 11. A computer program productas claimed in claim 1 in which the spurious mechanisms are rankedaccording to their significance and in which a range of availableintermediate frequencies is divided in to sub-ranges each identified bythe most significant spurious mechanism, if any, affecting the avoidanceband(s) and resulting from the use of an intermediate frequency in thatsub-range.
 12. A computer program product as claimed in claim 1 in whichthe spurious mechanisms include the first image.
 13. A computer programproduct as claimed in claim 1 in which the spurious mechanisms includelocal oscillator leakage.
 14. A computer program product as claimed inclaim 1 in which the spurious mechanisms include intermediate frequencyleakage.
 15. A computer program product as claimed in claim 1 in whichthe spurious mechanisms include the second harmonic of the localoscillator.
 16. A computer program product as claimed in claim 1 inwhich the spurious mechanisms include the third-order reverseinter-modulation product of the local oscillator and any external sourceof interference in the tuning band.
 17. A computer program product asclaimed in claim 8 including the step of determining one or moreadditional avoidance bands and repeating step (d) for each additionalavoidance band.
 18. A computer program product as claimed in claim 8 inwhich the spurious mechanisms are ranked according to their significanceand in which a range of available intermediate frequencies is divided into sub-ranges each identified by the most significant spuriousmechanism, if any, affecting the avoidance band(s) and resulting fromthe use of an intermediate frequency in that sub-range.
 19. A computerprogram product as claimed in claim 8 in which the spurious mechanismsinclude the first image.
 20. A computer program product as claimed inclaim 8 in which the spurious mechanisms include local oscillatorleakage.
 21. A computer program product as claimed in claim 8 in whichthe spurious mechanisms include intermediate frequency leakage.
 22. Acomputer program product as claimed in claim 8 in which the spuriousmechanisms include the second harmonic of the local oscillator.
 23. Acomputer program product as claimed in claim 8 in which the spuriousmechanisms include the third-order reverse inter-modulation product ofthe local oscillator and any external source of interference in thetuning band.
 24. Apparatus for determining an appropriate intermediatefrequency or intermediate frequency range for a radio frequency (r.f.)receiver in which a received modulated r.f. signal is mixed with asignal from a local oscillator at a different frequency to yield as oneof the mixing products a signal at a desired intermediate frequency forsubsequent processing, the apparatus comprising: a) means for receivinginput data defining a tuning band of radio frequencies which thereceiver is desired to receive; b) means for receiving input datadefining an avoidance band containing radio frequencies closed toexternal transmission and/or frequencies of sources of outsideinterference; c) means for storing data relating to a plurality ofspurious mechanisms by which the receiver either receives or transmitsspurious signals and determining the frequencies of the spurious signalsin relation to the intermediate frequency; d) means for determiningwhich intermediate frequencies result in spurious emissions to orresponses from the avoidance band for any of the frequencies of thetuning band.
 25. Apparatus as claimed in claim 24 in which said means(d) includes means for determining, for each spurious mechanism, one ormore hazard bands, being ranges of frequency of spurious emissions orresponses each corresponding to the whole of the tuning band. 26.Apparatus as claimed in claim 24 in which the spurious mechanismsinclude one of the second images.
 27. Apparatus as claimed in claim 24in which the spurious mechanisms include both of the second images. 28.Apparatus as claimed in any of claim 24 in which the spurious mechanismsinclude one of the third images.
 29. Apparatus as claimed in claim 24 inwhich the spurious mechanisms include both of the third images. 30.Apparatus as claimed in claim 24 in which the spurious mechanismsinclude the mixer sum product.
 31. Apparatus for determining anappropriate intermediate frequency for a radio frequency transmitter inwhich a modulated signal at an intermediate frequency is mixed with alocal oscillator waveform having a different frequency to yield as oneof the mixing products a signal at a desired frequency for transmission,the apparatus comprising: a) means for receiving input data defining atuning band of frequencies which the transmitter is desired to transmit;b) means for receiving input data defining an avoidance band containingradio frequencies closed to external transmission; c) means for storingdata relating to a plurality of spurious mechanisms by which thetransmitter transmits spurious signals and determining the relationshipbetween the spurious signals and the intermediate frequency; and d)means for determining which of the intermediate frequencies result inspurious emissions to the avoidance band for any of the frequencies inthe tuning band.
 32. Apparatus as claimed in claim 31 in which saidmeans include means for determining, for each spurious mechanism, one ormore hazard bands being ranges of frequency of spurious emissions eachcorresponding to the whole of the tuned band.
 33. Apparatus as claimedin claim 24 in which the spurious mechanisms are ranked in said means(c) according to their significance and in which a range of availableintermediate frequencies is divided in to sub-ranges each identified bythe most significant spurious mechanism, if any, affecting the avoidanceband(s) and resulting from the use of an intermediate frequency in thatsub-range.
 34. Apparatus as claimed in claim 31 in which the spuriousmechanisms are ranked in said means (c) according to their significanceand in which a range of available intermediate frequencies is divided into sub-ranges each identified by the most significant spuriousmechanism, if any, affecting the avoidance band(s) and resulting fromthe use of an intermediate frequency in that sub-range.
 35. Apparatus asclaimed in claim 33 in which said means (c) stores ranking data for thespurious mechanisms.
 36. Apparatus as claimed in claim 33 includingmeans for receiving input data relating to the ranking of the spuriousmechanisms.
 37. Apparatus as claimed in claim 24 in which the spuriousmechanisms include the first image.
 38. Apparatus as claimed in claim 24in which the spurious mechanisms include local oscillator leakage. 39.Apparatus as claimed in claim 24 in which the spurious mechanismsinclude intermediate frequency leakage.
 40. Apparatus as claimed inclaim 24 in which the spurious mechanisms include the second harmonic ofthe local oscillator.
 41. Apparatus as claimed in claim 24 in which thespurious mechanisms include the third-order reverse inter-modulationproduct of the local oscillator and any external source of interferencein the tuning band.
 42. Apparatus as claimed in claim 24 includingselection means for selecting a plurality of spurious mechanisms from alarger plurality of spurious mechanisms in said storing means (c) andinputting only said selection to said determining means.
 43. Apparatusas claimed in claim 31 in which the spurious mechanisms include thefirst image.
 44. Apparatus as claimed in claim 31 in which the spuriousmechanisms include local oscillator leakage.
 45. Apparatus as claimed inclaim 31 in which the spurious mechanisms include intermediate frequencyleakage.
 46. Apparatus as claimed in claim 31 in which the spuriousmechanisms include the second harmonic of the local oscillator. 47.Apparatus as claimed in claim 31 in which the spurious mechanismsinclude the third-order reverse inter-modulation product of the localoscillator and any external source of interference in the tuning band.48. Apparatus as claimed in claim 31 including selection means forselecting a plurality of spurious mechanisms from a larger plurality ofspurious mechanisms in said storing means (c) and inputting only saidselection to said determining means.
 49. A radio frequency receiverhaving means for receiving modulated r.f. signals, a mixer and a localoscillator, in which said mixer mixes said r.f, signals with signalsfrom said local oscillator to yield as one of the mixing products asignal at a desired intermediate frequency or a range of signals at arange of intermediate frequency for subsequent processing, said receiverfurther having apparatus according to claim 24 and means for changingthe intermediate frequency or intermediate frequency range in responseto said determining means to a frequency or range which minimisesspurious responses from or emissions to the avoidance band(s) for thewhole of the tuning range.
 50. A receiver as claimed in claim 49 havingmeans for receiving transmitted information relating to avoidance bandsand supplying said information to said means (b).
 51. A receiver asclaimed in claim 49 having means storing information relating toavoidance bands and geographical location and means for receivinggeographical location information to determine the appropriate avoidanceband(s).
 52. A receiver as claimed in claim 49 having means forreceiving transmitted geographical information.
 53. A receiver asclaimed in claim 49 in which said determining means comprises amicroprocessor.
 54. A receiver as claimed in claim 49 in which saidmeans for changing the intermediate frequency or frequency rangeoperates to change the frequency of the local oscillator.
 55. A receiveras claimed in claim 49 including band pass filter means for receivingthe mixer output and selecting signals at the intermediate frequency orrange, in which the pass band of said filter means is variable dependingon the intermediate frequency.
 56. A receiver as claimed in claim 55 inwhich the filter means comprises a plurality of band pass filters havingdifferent pass bands and switching means connecting a selected one ofsaid band pass filters to the output of the mixer.
 57. Apparatus asclaimed in claim 49 including tunable filter means for receiving themixer output and selecting signals at precise intermediate frequency.58. Apparatus as claimed in claim 57 in which said tunable filter meanscomprises a plurality of tunable filters having different tuning bandsencompassing a contiguous range of intermediate frequencies.
 59. A radiofrequency transceiver including a receiver as claimed in claim 49 and atransmitter, the transmitter including a mixer having an input connectedto a local oscillator for mixing signals for transmission with a localoscillator waveform having a different frequency to yield as one of themixing products a signal at a desired frequency for transmission,wherein said apparatus for determining an intermediate frequency (i.f.)or i.f. range for the receiver is also operable to determine an i.f. ori.f. range for the transmitter and wherein the transmitter has means forchanging the intermediate frequency in response to said determiningmeans to an i.f. or i.f. range which minimises spurious emissions to theavoidance band(s) for the whole of the tuning range.
 60. A transceiveras claimed in claim 59 in which the means for changing the transmitteri.f. operates to change the frequency of the transmitter localoscillator frequency.